36.15 Methods of Computation Bibliography B

Bibliography

♦A♦B♦C♦D♦E♦F♦G♦H♦I♦J♦K♦L♦M♦N♦O♦P♦Q♦R♦S♦T♦U♦V♦W♦X♦Y♦Z♦

J. Abad and J. Sesma (1995) Computation of the regular confluent hypergeometric function. The Mathematica Journal 5 (4), pp. 74–76.

External Links:

ISSN 1047-5974, FullText

Referenced by:

§13.32(iii).

Encodings:

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A. S. Abdullaev (1985) Asymptotics of solutions of the generalized sine-Gordon equation, the third Painlevé equation and the d’Alembert equation. Dokl. Akad. Nauk SSSR 280 (2), pp. 265–268 (Russian).

Notes:

English translation: Soviet Math. Dokl. 31(1985), no. 1, pp. 45–47

External Links:

ISSN 0002-3264, MathReview (M. S. Agranovich), ZentralBlatt

Referenced by:

§32.11(iv).

Encodings:

BibTeX
R. W. Abernathy and R. P. Smith (1993) Algorithm 724: Program to calculate F-percentiles. ACM Trans. Math. Software 19 (4), pp. 481–483.

Notes:

Double-precision Fortran, maximum accuracy 13D.

External Links:

ISSN 0098-3500, Document, TOMS module 724 (in GAMS), ZentralBlatt

Referenced by:

§8.28(iv).

Encodings:

BibTeX
M. J. Ablowitz and P. A. Clarkson (1991) Solitons, Nonlinear Evolution Equations and Inverse Scattering. London Mathematical Society Lecture Note Series, Vol. 149, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-38730-2, Document, Link, MathReview (Walter Oevel), ZentralBlatt

Referenced by:

§22.19(ii), §22.19(iii), §32.11(ii), §32.5, §9.16, Profile Mark J. Ablowitz, Profile Peter A. Clarkson.

Encodings:

BibTeX
M. J. Ablowitz and H. Segur (1977) Exact linearization of a Painlevé transcendent. Phys. Rev. Lett. 38 (20), pp. 1103–1106.

External Links:

Document, MathReview (Mark Adler)

Referenced by:

§32.11(ii), §32.13(i), §32.13(ii), §32.13(iii), §32.5.

Encodings:

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M. J. Ablowitz and H. Segur (1981) Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics, Vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

External Links:

ISBN 0-89871-174-6, MathReview (Benno Fuchssteiner), ZentralBlatt

Referenced by:

§21.9, §21.9, §32.5, §9.16, Profile Mark J. Ablowitz.

Encodings:

BibTeX
A. Abramov (1960) Tables of $\mathop{\ln\/}\nolimits\Gamma(z)$ for Complex Argument. Pergamon Press, New York.

External Links:

ZentralBlatt

Referenced by:

§5.22(iii).

Encodings:

BibTeX
M. Abramowitz and P. Rabinowitz (1954) Evaluation of Coulomb wave functions along the transition line. Physical Rev. (2) 96, pp. 77–79.

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§33.12(i).

Encodings:

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M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..

Notes:

Corrections appeared in later printings up to the 10th Printing, December, 1972. Reproductions by other publishers, in whole or in part, have been available since 1965.

External Links:

FullText, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§10.1, §10.21(ix), §10.47(i), §10.68(iv), §10.70, §10.75(ii), §10.75(xi), §10.75(iii), §10.75(iii), §10.75(iii), §10.75(iv), §10.75(v), §10.75(vii), §10.75(ix), Ch.10, §11.10(vi), §11.14(ii), §11.14(iii), Ch.11, §12.19, Ch.12, §13.30, Ch.13, §14.33, Ch.14, Ch.15, §18.14(i), §18.3, §18.41(i), §18.41(ii), §18.5(iv), §18.8, §19.1, §19.14(i), §19.14(ii), §19.25(v), §19.36(iii), §19.37(ii), §19.37(ii), §19.37(ii), §19.37(ii), §19.37(iii), §19.37(iii), §19.38, Ch.19, §20.15, Ch.20, §22.1, §22.15(ii), Ch.22, §23.1, §23.20(i), §23.23, §23.23, §23.9, §23.9, §23.9, Ch.23, §24.2(iv), §24.20, Ch.24, §25.19, §26.1, §26.1, §26.2, §26.21, §26.3(i), §26.4(i), §26.8(i), §27.2(ii), §27.21, §28.1, Ch.28, §30.1, Ch.30, §33.24, Ch.33, §4.44, §4.46, §5.11(i), §5.22(ii), §5.22(iii), §5.7(i), Ch.5, §6.19(ii), §6.19(iii), §6.20(i), Ch.6, §7.23(ii), §7.23(ii), §7.23(iii), Ch.7, 8.17.24, §8.22(ii), §8.26(iv), Ch.8, §9.18(ii), §9.18(iv), §9.18(v), §9.8(i), Ch.9, Profile Frank W. J. Olver, About the Project, Preface, Possible Errors in DLMF, Notations E, Notations E, Notations F, Notations F, Notations H, Notations H, Notations J, Notations K, Notations P, Notations P, Notations S, Notations Y, H. E. Fettis and J. C. Caslin (1973).

Encodings:

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M. Abramowitz (1949) Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

External Links:

MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§30.9(iii).

Encodings:

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M. Abramowitz (1954) Regular and irregular Coulomb wave functions expressed in terms of Bessel-Clifford functions. J. Math. Physics 33, pp. 111–116.

External Links:

MathReview (E. Weber), ZentralBlatt

Referenced by:

§33.9(ii).

Encodings:

BibTeX
J. Achenbach (1986) Numerik: Implementierung von Zylinderfunktionen. Elektrotechnik, Friedr. Vieweg & Sohn, Braunschweig-Wiesbaden.

External Links:

ISBN 3-528-04462-4, MathReview, ZentralBlatt

Referenced by:

§10.75(ii), §10.75(v).

Encodings:

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F. S. Acton (1974) Recurrence relations for the Fresnel integral $\int_{0}^{\infty}\frac{\mathop{\exp\/}\nolimits(-ct)dt}{\sqrt{t}(1+t^{2})}$ and similar integrals. Comm. ACM 17 (8), pp. 480–481.

External Links:

ISSN 0001-0782, Document, MathReview, ZentralBlatt

Referenced by:

§6.18(ii).

Encodings:

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J. A. Adam (2002) The mathematical physics of rainbows and glories. Phys. Rep. 356 (4-5), pp. 229–365 (English).

External Links:

Document, FullText, ZentralBlatt

Referenced by:

§9.16, §9.16.

Encodings:

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V. S. Adamchik and H. M. Srivastava (1998) Some series of the zeta and related functions. Analysis (Munich) 18 (2), pp. 131–144.

External Links:

ISSN 0174-4747, MathReview (Jack Quine), ZentralBlatt

Referenced by:

§25.11(xi), §25.8.

Encodings:

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V. S. Adamchik (1998) Polygamma functions of negative order. J. Comput. Appl. Math. 100 (2), pp. 191–199.

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§25.11(viii).

Encodings:

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A. G. Adams (1969) Algorithm 39: Areas under the normal curve. The Computer Journal 12 (2), pp. 197–198.

Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

Document

Referenced by:

§7.25(ii).

Encodings:

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J. C. Adams and P. N. Swarztrauber (1997) SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.

Notes:

SPHEREPACK 2.0 is a collection of Fortran programs that facilitates computer modeling of geophysical processes. Accurate solutions are obtained via the spectral method that uses both scalar and vector spherical harmonic transforms. The package also contains utility programs for computing the associated Legendre functions. SPHEREPACK 3.1 was released in August 2003.

External Links:

FullText, SPHEREPACK 3.1

Referenced by:

§14.34(ii).

Encodings:

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A. Adelberg (1992) On the degrees of irreducible factors of higher order Bernoulli polynomials. Acta Arith. 62 (4), pp. 329–342.

External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

Encodings:

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A. Adelberg (1996) Congruences of $p$ -adic integer order Bernoulli numbers. J. Number Theory 59 (2), pp. 374–388.

External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

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C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson (1985) Chapter $16$ of Ramanujan’s second notebook: Theta-functions and $q$ -series. Mem. Amer. Math. Soc. 53 (315), pp. v+85.

External Links:

ISSN 0065-9266, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§20.11(ii).

Encodings:

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C. L. Adler, J. A. Lock, B. R. Stone and C. J. Garcia (1997) High-order interior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder. J. Opt. Soc. Amer. A 14 (6), pp. 1305–1315.

External Links:

FullText

Referenced by:

§36.14(ii).

Encodings:

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V. È. Adler (1994) Nonlinear chains and Painlevé equations. Phys. D 73 (4), pp. 335–351.

External Links:

ISSN 0167-2789, Document, MathReview (F. Pempinelli), ZentralBlatt

Referenced by:

§32.2(v).

Encodings:

BibTeX
P. Adrian (1959) Die Bezeichnungsweise der Bernoullischen Zahlen. Mitt. Verein. Schweiz. Versicherungsmath. 59, pp. 199–206 (German).

External Links:

MathReview (L. Moser), ZentralBlatt

Referenced by:

§24.1.

Encodings:

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T. Agoh and K. Dilcher (2011) Integrals of products of Bernoulli polynomials. J. Math. Anal. Appl. 381 (1), pp. 10–16.

External Links:

ISSN 0022-247X, Document, FullText, MathReview (Pablo Manuel Román), ZentralBlatt

Referenced by:

§24.13(i), §24.13(i).

Encodings:

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M. M. Agrest, S. I. Labakhua, M. M. Rikenglaz and Ts. Sh. Chachibaya (1982) Tablitsy funktsii Struve i integralov ot nikh. “Nauka”, Moscow (Russian).

Notes:

Translated title: Tables of Struve Functions and their Integrals

External Links:

MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§11.14(ii), §11.14(iii).

Encodings:

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M. M. Agrest and M. S. Maksimov (1971) Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

External Links:

MathReview, ZentralBlatt

Referenced by:

§11.14(v).

Encodings:

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L. V. Ahlfors (1966) Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

Notes:

A third edition was published in 1978 by McGraw-Hill, New York.

External Links:

MathReview (P. Lelong), ZentralBlatt

Referenced by:

§1.9(iii), §23.18.

Encodings:

BibTeX
A. R. Ahmadi and S. E. Widnall (1985) Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

External Links:

Document, ZentralBlatt

Referenced by:

§11.12.

Encodings:

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S. Ahmed and M. E. Muldoon (1980) On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

External Links:

ISSN 0024-1318, MathReview (James M. Horner)

Referenced by:

§13.9(i).

Encodings:

BibTeX
S-H. Ahn, H. Lee and H. M. Lee (2001) Ly $\alpha$ line formation in starbursting galaxies. I. Moderately thick, dustless, and static H i media. Astrophysical J. 554, pp. 604–614.

External Links:

FullText

Referenced by:

§7.21.

Encodings:

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H. Airault, H. P. McKean and J. Moser (1977) Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem. Comm. Pure Appl. Math. 30 (1), pp. 95–148.

External Links:

MathReview (Alexander A. Pankov), ZentralBlatt

Referenced by:

§23.21(ii).

Encodings:

BibTeX
H. Airault (1979) Rational solutions of Painlevé equations. Stud. Appl. Math. 61 (1), pp. 31–53.

External Links:

ISSN 0022-2526, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§32.10(ii), §32.8(i), §32.8(v).

Encodings:

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G. B. Airy (1838) On the intensity of light in the neighbourhood of a caustic. Trans. Camb. Phil. Soc. 6, pp. 379–402.

Referenced by:

§9.16, §9.16.

Encodings:

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G. B. Airy (1849) Supplement to a paper “On the intensity of light in the neighbourhood of a caustic”. Trans. Camb. Phil. Soc. 8, pp. 595–599.

Referenced by:

§9.16.

Encodings:

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N. I. Akhiezer (1988) Lectures on Integral Transforms. Translations of Mathematical Monographs, Vol. 70, American Mathematical Society, Providence, RI.

Notes:

Translated from the Russian by H. H. McFaden

External Links:

ISBN 0-8218-4524-1, MathReview, ZentralBlatt

Referenced by:

§10.22(v).

Encodings:

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N. I. Akhiezer (1990) Elements of the Theory of Elliptic Functions. Translations of Mathematical Monographs, Vol. 79, American Mathematical Society, Providence, RI.

Notes:

Translated from the second Russian edition by H. H. McFaden

External Links:

ISBN 0-8218-4532-2, MathReview (Glenn Stevens), ZentralBlatt

Referenced by:

§22.18(ii), §22.18(iv).

Encodings:

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S. V. Aksenov, M. A. Savageau, U. D. Jentschura, J. Becher, G. Soff and P. J. Mohr (2003) Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

Notes:

Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.

External Links:

Code, Document

Referenced by:

§25.21(viii).

Encodings:

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A. M. Al-Rashed and N. Zaheer (1985) Zeros of Stieltjes and Van Vleck polynomials and applications. J. Math. Anal. Appl. 110 (2), pp. 327–339.

External Links:

ISSN 0022-247X, Document, MathReview (Evangelos Ifantis), ZentralBlatt

Referenced by:

§31.15(ii).

Encodings:

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W. A. Al-Salam and L. Carlitz (1959) Some determinants of Bernoulli, Euler and related numbers. Portugal. Math. 18, pp. 91–99.

External Links:

FullText, MathReview (D. P. Banerjee), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

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W. A. Al-Salam and L. Carlitz (1965) Some orthogonal $q$ -polynomials. Math. Nachr. 30, pp. 47–61.

External Links:

ISSN 0025-584X, Document, MathReview (A. E. Danese), ZentralBlatt

Referenced by:

§18.27(vii).

Encodings:

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W. A. Al-Salam and M. E. H. Ismail (1994) A $q$ -beta integral on the unit circle and some biorthogonal rational functions. Proc. Amer. Math. Soc. 121 (2), pp. 553–561.

External Links:

ISSN 0002-9939, FullText, MathReview (S. P. Goyal), ZentralBlatt

Referenced by:

§18.33(v).

Encodings:

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M. Alam (1979) Zeros of Stieltjes and Van Vleck polynomials. Trans. Amer. Math. Soc. 252, pp. 197–204.

External Links:

ISSN 0002-9947, FullText, MathReview (Pet”r Rusev), ZentralBlatt

Referenced by:

§31.15(ii).

Encodings:

BibTeX
D. W. Albrecht, E. L. Mansfield and A. E. Milne (1996) Algorithms for special integrals of ordinary differential equations. J. Phys. A 29 (5), pp. 973–991.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§32.10(i).

Encodings:

BibTeX
J. R. Albright and E. P. Gavathas (1986) Integrals involving Airy functions. J. Phys. A 19 (13), pp. 2663–2665.

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§9.11(iv).

Encodings:

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J. R. Albright (1977) Integrals of products of Airy functions. J. Phys. A 10 (4), pp. 485–490.

External Links:

Document, MathReview (Y. L. Luke), ZentralBlatt

Referenced by:

§9.11(iv), §9.11(iv).

Encodings:

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K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther (1956) Study of nuclear structure by electromagnetic excitation with accelerated ions. Rev. Mod. Phys. 28, pp. 432–542.

External Links:

ISSN 0034-6861, Document, MathReview, ZentralBlatt

Referenced by:

§33.22(ii).

Encodings:

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G. Alefeld and J. Herzberger (1983) Introduction to Interval Computations. Computer Science and Applied Mathematics, Academic Press Inc., New York.

Notes:

Translated from the German by Jon Rokne

External Links:

ISBN 0-12-049820-0, MathReview (H. Ratschek), ZentralBlatt

Referenced by:

§3.1(ii).

Encodings:

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W. R. Alford, A. Granville and C. Pomerance (1994) There are infinitely many Carmichael numbers. Ann. of Math. (2) 139 (3), pp. 703–722.

External Links:

ISSN 0003-486X, FullText, MathReview (H. L. Montgomery), ZentralBlatt

Referenced by:

§27.12.

Encodings:

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F. Alhargan and S. Judah (1992) Frequency response characteristics of the multiport planar elliptic patch. IEEE Trans. Microwave Theory Tech. 40 (8), pp. 1726–1730.

External Links:

Document

Referenced by:

§28.33(ii).

Encodings:

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F. Alhargan and S. Judah (1995) A general mode theory for the elliptic disk microstrip antenna. IEEE Trans. Antennas and Propagation 43 (6), pp. 560–568.

External Links:

Document

Referenced by:

§28.33(ii).

Encodings:

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F. A. Alhargan (2000) Algorithm 804: Subroutines for the computation of Mathieu functions of integer orders. ACM Trans. Math. Software 26 (3), pp. 408–414.

Notes:

Double-precision C++, minimum accuracy 14D

External Links:

ISSN 0098-3500, Document, TOMS module 804 (in GAMS)

Referenced by:

§28.36(ii), §28.36(iii).

Encodings:

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G. Allasia and R. Besenghi (1987a) Numerical computation of Tricomi’s psi function by the trapezoidal rule. Computing 39 (3), pp. 271–279.

External Links:

ISSN 0010-485X, Document, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

Encodings:

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G. Allasia and R. Besenghi (1991) Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.

External Links:

ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

Encodings:

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G. Allasia and R. Besenghi (1987b) Numerical calculation of incomplete gamma functions by the trapezoidal rule. Numer. Math. 50 (4), pp. 419–428.

External Links:

ISSN 0029-599X, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§8.25(ii).

Encodings:

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G. Allasia and R. Besenghi (1989) Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule. In Numerical and Applied Mathematics, Part II (Paris, 1988), C. Brezinski (Ed.), IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.

External Links:

MathReview

Referenced by:

§25.18(i).

Encodings:

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G. Almkvist and B. Berndt (1988) Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, $\pi$ , and the Ladies Diary. Amer. Math. Monthly 95 (7), pp. 585–608.

External Links:

ISSN 0002-9890, FullText, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

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Z. Altaç (1996) Integrals involving Bickley and Bessel functions in radiative transfer, and generalized exponential integral functions. J. Heat Transfer 118 (3), pp. 789–792.

External Links:

Document

Referenced by:

§10.73(iv), §8.24(iii).

Encodings:

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H. H. Aly, H. J. W. Müller-Kirsten and N. Vahedi-Faridi (1975) Scattering by singular potentials with a perturbation – Theoretical introduction to Mathieu functions. J. Mathematical Phys. 16, pp. 961–970.

Notes:

Erratum: same journal 17 (1975), no. 7, p. 1361

External Links:

Document, MathReview (K. Veselic), ZentralBlatt

Referenced by:

§28.33(iii).

Encodings:

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H. Alzer and S. Qiu (2004) Monotonicity theorems and inequalities for the complete elliptic integrals. J. Comput. Appl. Math. 172 (2), pp. 289–312.

External Links:

ISSN 0377-0427, Document, MathReview (Živorad Tomovski), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

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H. Alzer (1997a) A harmonic mean inequality for the gamma function. J. Comput. Appl. Math. 87 (2), pp. 195–198.

Notes:

For corrigendum see same journal v. 90 (1998), no. 2, p. 265

External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§5.6(i).

Encodings:

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H. Alzer (1997b) On some inequalities for the incomplete gamma function. Math. Comp. 66 (218), pp. 771–778.

External Links:

ISSN 0025-5718, Document, MathReview, ZentralBlatt

Referenced by:

§8.10.

Encodings:

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H. Alzer (2000) Sharp bounds for the Bernoulli numbers. Arch. Math. (Basel) 74 (3), pp. 207–211.

External Links:

ISSN 0003-889X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.9.

Encodings:

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H. Alzer (2008) Gamma function inequalities. Numer. Algorithms 49 (1-4), pp. 53–84.

External Links:

ISSN 1017-1398, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§5.6(i), §5.6(i).

Encodings:

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D. E. Amos, S. L. Daniel and M. K. Weston (1977) Algorithm 511: CDC 6600 subroutines IBESS and JBESS for Bessel functions $I_{\nu}(x)$ and $J_{\nu}(x)$ , $x\geq 0$ , $\nu\geq 0$ . ACM Trans. Math. Software 3 (1), pp. 93–95.

Notes:

Single-precision Fortran, maximum accuracy 16S.

External Links:

ISSN 0098-3500, Document, Companion paper. Erratum. TOMS module 511 (in GAMS)

Referenced by:

§10.77(iii), §9.20(ii).

Encodings:

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D. E. Amos (1974) Computation of modified Bessel functions and their ratios. Math. Comp. 28 (125), pp. 239–251.

External Links:

ISSN 0025-5718, FullText, MathReview (L. Lorch), ZentralBlatt

Referenced by:

§10.74(v).

Encodings:

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D. E. Amos (1983a) Algorithm 609. A portable FORTRAN subroutine for the Bickley functions ${\rm Ki}_{n}(x)$ . ACM Trans. Math. Software 9 (4), pp. 480–493.

Notes:

Single-precision Fortran, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, TOMS module 609 (in GAMS), MathReview (Marietta J. Tretter), ZentralBlatt

Referenced by:

§10.77(ix).

Encodings:

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D. E. Amos (1983b) Algorithm 610. A portable FORTRAN subroutine for derivatives of the psi function. ACM Trans. Math. Software 9 (4), pp. 494–502.

Notes:

Single and double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, TOMS module 610 (in GAMS), MathReview Entry, ZentralBlatt

Referenced by:

§5.24(iii).

Encodings:

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D. E. Amos (1983c) Uniform asymptotic expansions for exponential integrals $E_{n}(x)$ and Bickley functions ${\rm{K}i}_{n}(x)$ . ACM Trans. Math. Software 9 (4), pp. 467–479.

External Links:

ISSN 0098-3500, Document, MathReview (Marietta J. Tretter), ZentralBlatt

Referenced by:

§10.43(iii).

Encodings:

BibTeX
D. E. Amos (1985) A subroutine package for Bessel functions of a complex argument and nonnegative order. Technical Report Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.

External Links:

FullText

Referenced by:

§10.75(iii), B. Döring (1966).

Encodings:

BibTeX
D. E. Amos (1986) Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12 (3), pp. 265–273.

Notes:

Single and double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark #1. Remark #2. TOMS module 644 (in GAMS), MathReview Entry, ZentralBlatt

Referenced by:

§10.77(v), §5.24(ii), §9.20(ii), §9.20(iii).

Encodings:

BibTeX
D. E. Amos (1980a) Algorithm 556: Exponential integrals. ACM Trans. Math. Software 6 (3), pp. 420–428.

Notes:

Single-precision Fortran, maximum accuracy 14S. For a Remark see same journal v. 9 (1983), no. 4, p. 525.

External Links:

ISSN 0098-3500, Document, Remark,TOMS module 556 (in GAMS), ZentralBlatt

Referenced by:

§6.21(ii), §8.28(vi).

Encodings:

BibTeX
D. E. Amos (1980b) Computation of exponential integrals. ACM Trans. Math. Software 6 (3), pp. 365–377.

External Links:

ISSN 0098-3500, Document, MathReview (M. M. Chawla), ZentralBlatt

Referenced by:

§8.25(v).

Encodings:

BibTeX
D. E. Amos (1989) Repeated integrals and derivatives of $K$ Bessel functions. SIAM J. Math. Anal. 20 (1), pp. 169–175.

External Links:

ISSN 0036-1410, Document, MathReview (A. Haimovici), ZentralBlatt

Referenced by:

§10.43(iii).

Encodings:

BibTeX
D. E. Amos (1990) Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Software 16 (2), pp. 178–182.

Notes:

Double- and single-precision Fortran, maximum accuracy 18S or 14S.

External Links:

ISSN 0098-3500, Document, TOMS module 683 (in GAMS), MathReview, ZentralBlatt

Referenced by:

§6.21(iii), §8.28(vii).

Encodings:

BibTeX
G. D. Anderson, S.-L. Qiu, M. K. Vamanamurthy and M. Vuorinen (2000) Generalized elliptic integrals and modular equations. Pacific J. Math. 192 (1), pp. 1–37.

External Links:

ISSN 0030-8730, FullText, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.35(i).

Encodings:

BibTeX
G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen (1990) Functional inequalities for complete elliptic integrals and their ratios. SIAM J. Math. Anal. 21 (2), pp. 536–549.

External Links:

ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX
G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen (1992a) Functional inequalities for hypergeometric functions and complete elliptic integrals. SIAM J. Math. Anal. 23 (2), pp. 512–524.

External Links:

ISSN 0036-1410, Document, MathReview (J. M. H. Peters), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX
G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen (1992b) Hypergeometric Functions and Elliptic Integrals. In Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (Eds.), pp. 48–85.

External Links:

MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX
G. D. Anderson and M. K. Vamanamurthy (1985) Inequalities for elliptic integrals. Publ. Inst. Math. (Beograd) (N.S.) 37(51), pp. 61–63.

External Links:

ISSN 0350-1302, MathReview, ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX
G. D. Anderson, M. K. Vamanamurthy and M. K. Vuorinen (1997) Conformal Invariants, Inequalities, and Quasiconformal Maps. John Wiley & Sons Inc., New York.

Notes:

With PC diskette, a Wiley-Interscience Publication

External Links:

ISBN 0-471-59486-5, MathReview (H. Renelt), ZentralBlatt

Referenced by:

§15.17(ii), §19.9(i).

Encodings:

BibTeX

W. L. Anderson (1982) Algorithm 588. Fast Hankel transforms using related and lagged convolutions. ACM Trans. Math. Software 8 (4), pp. 369–370.

Notes:

Single-precision Fortran, maximum accuracy 8S.

External Links:

ISSN 0098-3500, Document, TOMS module 588 (in GAMS)

Referenced by:

§10.77(ix).

Encodings:

BibTeX
F. V. Andreev and A. V. Kitaev (2002) Transformations $RS^{2}_{4}(3)$ of the ranks $\leq 4$ and algebraic solutions of the sixth Painlevé equation. Comm. Math. Phys. 228 (1), pp. 151–176.

External Links:

ISSN 0010-3616, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.9(iii).

Encodings:

BibTeX
G. E. Andrews and A. Berkovich (1998) A trinomial analogue of Bailey’s lemma and $N=2$ superconformal invariance. Comm. Math. Phys. 192 (2), pp. 245–260.

External Links:

ISSN 0010-3616, Document, MathReview (Anne Schilling), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX
G. E. Andrews (1966a) On basic hypergeometric series, mock theta functions, and partitions. II. Quart. J. Math. Oxford Ser. (2) 17, pp. 132–143.

External Links:

Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§17.6(ii).

Encodings:

BibTeX
G. E. Andrews, R. A. Askey, B. C. Berndt and R. A. Rankin (Eds.) (1988) Ramanujan Revisited. Academic Press Inc., Boston, MA.

External Links:

ISBN 0-12-058560-X, ISBN 0-12-058560-X, MathReview, ZentralBlatt

Referenced by:

§20.11(ii), Profile Richard A. Askey.

Encodings:

BibTeX
G. E. Andrews, R. Askey and R. Roy (1999) Special Functions. Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-62321-9, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§1.10(vii), §1.15(iii), §1.15(vi), §1.15(vii), §10.22(vi), §13.6(v), §13.9(i), Ch.13, §14.3(iii), §14.30(iv), §15.10(i), §15.11(i), §15.11(ii), §15.14, §15.17(iv), §15.2(i), §15.4(ii), §15.5(i), §15.5(ii), §15.6, §15.7, §15.8(iv), §15.8(iii), Ch.15, §16.4(ii), §16.4(iii), §16.4(v), §16.4(v), Ch.16, §17.12, Ch.17, §18.10(ii), §18.10(iv), §18.11(i), §18.12, §18.17(iv), §18.17(viii), §18.18(iv), §18.18(v), §18.18(vii), §18.2(i), §18.2(iv), §18.2(vi), §18.20(ii), §18.22(i), §18.25(ii), §18.26(i), §18.3, §18.38(ii), §18.5(iii), Ch.18, §26.19, §4.10(i), §4.10(ii), §5.13, §5.14, §5.16, §5.16, §5.18(i), §5.18(ii), §5.18(iii), §5.20, §5.4(ii), §5.5(iv), Ch.5, Ch.6, Profile Richard A. Askey, Profile Ranjan Roy.

Encodings:

BibTeX
G. E. Andrews and D. Foata (1980) Congruences for the $q$ -secant numbers. European J. Combin. 1 (4), pp. 283–287.

External Links:

ISSN 0195-6698, MathReview (J. E. Cigler), ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

BibTeX
G. E. Andrews, I. P. Goulden and D. M. Jackson (1986) Shanks’ convergence acceleration transform, Padé approximants and partitions. J. Combin. Theory Ser. A 43 (1), pp. 70–84.

External Links:

ISSN 0097-3165, Document, MathReview (Kenneth A. Jukes), ZentralBlatt

Referenced by:

§17.18.

Encodings:

BibTeX
G. E. Andrews (1966b) $q$ -identities of Auluck, Carlitz, and Rogers. Duke Math. J. 33 (3), pp. 575–581.

External Links:

Document, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§17.9(iv).

Encodings:

BibTeX
G. E. Andrews (1972) Summations and transformations for basic Appell series. J. London Math. Soc. (2) 4, pp. 618–622.

External Links:

MathReview (R. N. Jain), ZentralBlatt

Referenced by:

§17.11.

Encodings:

BibTeX
G. E. Andrews (1974) Applications of basic hypergeometric functions. SIAM Rev. 16 (4), pp. 441–484.

External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§17.16, Ch.17.

Encodings:

BibTeX
G. E. Andrews (1976) The Theory of Partitions. Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, MA-London-Amsterdam.

Notes:

Reprinted by Cambridge University Press, Cambridge, 1998.

External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§17.18, §17.2(iii), §17.2(vi), §17.5, Ch.17, §26.10(ii), §26.10(iii), §26.10(iv), §26.10(v), §26.10(vi), §26.11, §26.12(iv), §26.14(i), §26.14(ii), §26.16, §26.16, §26.21, §26.9(i), §26.9(i), §26.9(ii), §26.9(iv), §27.14(vi), Ch.27.

Encodings:

BibTeX
G. E. Andrews (1979) Plane partitions. III. The weak Macdonald conjecture. Invent. Math. 53 (3), pp. 193–225.

External Links:

ISSN 0020-9910, Document, MathReview (Edward A. Bender), ZentralBlatt

Referenced by:

§26.12(i), §26.12(ii).

Encodings:

BibTeX
G. E. Andrews (1984) Multiple series Rogers-Ramanujan type identities. Pacific J. Math. 114 (2), pp. 267–283.

External Links:

ISSN 0030-8730, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX
G. E. Andrews (1986) $q$ -Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra. CBMS Regional Conference Series in Mathematics, Vol. 66, Amer. Math. Soc., Providence, RI.

External Links:

ISBN 0-8218-0716-1, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.14, §17.14, §17.16, Ch.17, Profile George E. Andrews.

Encodings:

BibTeX
G. E. Andrews (1996) Pfaff’s method II: Diverse applications. J. Comput. Appl. Math. 68 (1-2), pp. 15–23.

External Links:

ISSN 0377-0427, Document, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

§17.7(iii).

Encodings:

BibTeX
G. E. Andrews (2000) Umbral calculus, Bailey chains, and pentagonal number theorems. J. Combin. Theory Ser. A 91 (1-2), pp. 464–475.

Notes:

In memory of Gian-Carlo Rota

External Links:

ISSN 0097-3165, Document, MathReview (Alessandro Di Bucchianico), ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX
G. E. Andrews (2001) Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.

External Links:

ISBN 0-7923-7119-4, MathReview, ZentralBlatt

Referenced by:

§17.12.

Encodings:

BibTeX
H. M. Antia (1993) Rational function approximations for Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 84, pp. 101–108.

Notes:

Double-precision Fortran, maximum precision 8D.

External Links:

ISSN 0067-0049, Document, Code

Referenced by:

§25.20, §25.21(vii).

Encodings:

BibTeX
M. A. Anuta, D. W. Lozier and P. R. Turner (1996) The MasPar MP-1 as a computer arithmetic laboratory. J. Res. Nat. Inst. Stand. Technol. 101 (2), pp. 165–174.

External Links:

Document

Referenced by:

§3.1(iv).

Encodings:

BibTeX
K. Aomoto (1987) Special value of the hypergeometric function $\mathop{{{}_{3}F_{2}}\/}\nolimits$ and connection formulae among asymptotic expansions. J. Indian Math. Soc. (N.S.) 51, pp. 161–221.

External Links:

ISSN 0019-5839, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§16.4(iii).

Encodings:

BibTeX
A. Apelblat (1983) Table of Definite and Infinite Integrals. Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.

Notes:

Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1386.

External Links:

ISBN 0-444-42151-3, MathReview (R. P. Boas), ZentralBlatt

Referenced by:

§1.4(iv), §10.22(vi), §10.43(vi), §11.7(v), §11.9(iv), §12.5(iv), §13.10(vi), §13.23(v), §15.14, §16.20, §16.5, §18.17(ix), §4.10(iii), §4.26(v), §4.40(v), §5.13, §6.14(iii), §7.14(iii), §8.14, §8.19(x).

Encodings:

BibTeX
A. Apelblat (1989) Derivatives and integrals with respect to the order of the Struve functions $\mathop{\mathbf{H}_{\nu}\/}\nolimits(x)$ and $\mathop{\mathbf{L}_{\nu}\/}\nolimits(x)$ . J. Math. Anal. Appl. 137 (1), pp. 17–36.

External Links:

ISSN 0022-247X, Document, MathReview (A. McD. Mercer), ZentralBlatt

Referenced by:

§11.4(vi), §11.7(iv).

Encodings:

BibTeX
A. Apelblat (1991) Integral representation of Kelvin functions and their derivatives with respect to the order. Z. Angew. Math. Phys. 42 (5), pp. 708–714.

External Links:

ISSN 0044-2275, Document, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§10.61(v), §10.64.

Encodings:

BibTeX
T. M. Apostol and I. Niven (1994) Number Theory. In The New Encyclopaedia Britannica, Vol. 25, pp. 14–37.

Referenced by:

§27.13(i), §27.15, §27.16, Ch.27.

Encodings:

BibTeX
T. M. Apostol and H. S. Zuckerman (1951) On magic squares constructed by the uniform step method. Proc. Amer. Math. Soc. 2 (4), pp. 557–565.

External Links:

ISSN 0002-9939, Fulltext, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§27.17.

Encodings:

BibTeX
T. M. Apostol (1952) Theorems on generalized Dedekind sums. Pacific J. Math. 2 (1), pp. 1–9.

External Links:

MathReview (N. G. de Bruijn), ZentralBlatt

Referenced by:

§25.11(xii).

Encodings:

BibTeX
T. M. Apostol and T. H. Vu (1984) Dirichlet series related to the Riemann zeta function. J. Number Theory 19 (1), pp. 85–102.

External Links:

ISSN 0022-314X, Document, MathReview (Kai Man Tsang), ZentralBlatt

Referenced by:

§25.16(ii), §25.16(ii).

Encodings:

BibTeX
T. M. Apostol (1976) Introduction to Analytic Number Theory. Springer-Verlag, New York.

Notes:

Undergraduate Texts in Mathematics

External Links:

MathReview (E. Grosswald), ZentralBlatt

Referenced by:

§24.13(i), §24.17(iii), §24.5(ii), §24.8(i), §25.10(ii), §25.11(i), §25.11(x), §25.11(iii), §25.11(iv), §25.11(v), §25.11(vii), §25.13, §25.15(i), §25.15(ii), §25.16(i), §25.2(i), §25.2(ii), §25.2(iii), §25.2(iv), §25.4, §25.5(i), §25.5(iii), §25.6(i), Ch.25, §27.10, §27.11, §27.13(i), §27.13(iii), §27.13(iv), §27.14(i), §27.14(ii), §27.14(v), §27.2(i), §27.3, §27.4, §27.5, §27.5, §27.6, §27.8, §27.9, Ch.27.

Encodings:

BibTeX
T. M. Apostol (1983) A proof that Euler missed: Evaluating $\mathop{\zeta\/}\nolimits(2)$ the easy way. Math. Intelligencer 5 (3), pp. 59–60.

External Links:

ISSN 0343-6993, MathReview (P. Szüsz), ZentralBlatt

Referenced by:

§25.6(i).

Encodings:

BibTeX
T. M. Apostol (1985a) Formulas for higher derivatives of the Riemann zeta function. Math. Comp. 44 (169), pp. 223–232.

External Links:

ISSN 0025-5718, FullText, MathReview (Aleksandar Ivić), ZentralBlatt

Referenced by:

§25.11(iii), §25.11(vi), §25.18(i), 25.4.5, §25.4, §25.6(ii).

Encodings:

BibTeX
T. M. Apostol (1985b) Note on the trivial zeros of Dirichlet $L$ -functions. Proc. Amer. Math. Soc. 94 (1), pp. 29–30.

External Links:

ISSN 0002-9939, FullText, MathReview (Jerzy Kaczorowski), ZentralBlatt

Referenced by:

§25.15(ii).

Encodings:

BibTeX
T. M. Apostol (1990) Modular Functions and Dirichlet Series in Number Theory. 2nd edition, Graduate Texts in Mathematics, Vol. 41, Springer-Verlag, New York.

External Links:

ISBN 0-387-97127-0, MathReview, ZentralBlatt

Referenced by:

§23.10(iv), §23.15(i), §23.17(ii), §23.18, §23.18, §23.19, §23.20(i), §23.20(v), Ch.23, §27.14(iii), §27.14(iv), §27.14(vi), §27.7, Ch.27.

Encodings:

BibTeX
T. M. Apostol (2000) A Centennial History of the Prime Number Theorem. In Number Theory, Trends Math., pp. 1–14.

External Links:

MathReview (Giovanni Coppola), ZentralBlatt

Referenced by:

§25.16(i).

Encodings:

BibTeX
T. M. Apostol (2006) Bernoulli’s power-sum formulas revisited. Math. Gaz. 90 (518), pp. 276–279.

Referenced by:

§24.4(iii).

Encodings:

BibTeX
T. M. Apostol (2008) A primer on Bernoulli numbers and polynomials. Math. Mag. 81 (3), pp. 178–190.

External Links:

ISSN 0025-570X, MathReview Entry

Referenced by:

§24.5(ii), Ch.24.

Encodings:

BibTeX
H. Appel (1968) Numerical Tables for Angular Correlation Computations in $\alpha$ -, $\beta$ - and $\gamma$ -Spectroscopy: $3j$ -, $6j$ -, $9j$ -Symbols, F- and $\Gamma$ -Coefficients. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology, Springer-Verlag.

External Links:

ISBN 978-3-540-04218-1

Referenced by:

§34.14.

Encodings:

BibTeX
P. Appell and J. Kampé de Fériet (1926) Fonctions hypergéométriques et hypersphériques. Polynomes d’Hermite. Gauthier-Villars, Paris.

External Links:

ZentralBlatt

Referenced by:

§16.13, §16.15, Ch.16.

Encodings:

BibTeX
R. W. B. Ardill and K. J. M. Moriarty (1978) Spherical Bessel functions $j_{n}$ and $y_{n}$ of integer order and real argument. Comput. Phys. Comm. 14 (3-4), pp. 261–265.

Notes:

Single-precision Fortran, maximum accuracy 10S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

§10.77(ii).

Encodings:

BibTeX
G. B. Arfken and H. J. Weber (2005) Mathematical Methods for Physicists. 6th edition, Elsevier, Oxford.

External Links:

ISBN 0-12-059876-0;0-12-088584-0, MathReview, ZentralBlatt

Referenced by:

§1.17(ii), §1.17(iii).

Encodings:

BibTeX
J. V. Armitage and W. F. Eberlein (2006) Elliptic Functions. London Mathematical Society Student Texts, Vol. 67, Cambridge University Press, Cambridge.

External Links:

ISBN 978-0-521-78078-0; 978-0-521-78563-1; 0-521-78563-4, Document, MathReview (Shaun Cooper), ZentralBlatt

Referenced by:

Ch.19, Ch.20, Ch.22, Ch.23.

Encodings:

BibTeX
J. V. Armitage (1989) The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.

External Links:

MathReview, ZentralBlatt

Referenced by:

§25.17.

Encodings:

BibTeX
B. H. Armstrong (1967) Spectrum line profiles: The Voigt function. J. Quant. Spectrosc. Radiat. Transfer 7, pp. 61–88.

External Links:

Document

Referenced by:

§7.19(iv), §7.21.

Encodings:

BibTeX
V. I. Arnol ${}^{\prime}$ d (1997) Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, Vol. 60, Springer-Verlag, New York.

Notes:

Translated from the 1974 Russian original by K. Vogtmann and A. Weinstein, Corrected reprint of the second (1989) edition

External Links:

ISBN 0-387-96890-3, MathReview

Referenced by:

§21.5(i).

Encodings:

BibTeX
V. I. Arnol’d, S. M. Guseĭn-Zade and A. N. Varchenko (1988) Singularities of Differentiable Maps. Vol. II. Birkhäuser, Boston-Berlin.

Notes:

Monodromy and asymptotics of integrals, Translated from the Russian by Hugh Porteous, Translation revised by the authors and James Montaldi

External Links:

ISBN 0-8176-3185-2, MathReview, ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

BibTeX
V. I. Arnol’d (1972) Normal forms of functions near degenerate critical points, the Weyl groups ${A}_{k},{D}_{k},{E}_{k}$ and Lagrangian singularities. Funkcional. Anal. i Priložen. 6 (4), pp. 3–25 (Russian).

Notes:

In Russian. English translation: Functional Anal. Appl., 6(1973), pp. 254–272.

External Links:

MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

Encodings:

BibTeX
V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

Notes:

Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.

External Links:

Document, MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

Encodings:

BibTeX
V. I. Arnol’d (1975) Critical points of smooth functions, and their normal forms. Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).

Notes:

In Russian. English translation: Russian Math. Surveys, 30(1975), no. 5, pp. 1–75.

External Links:

Document, MathReview (D. Siersma), ZentralBlatt

Referenced by:

§36.2(i), Ch.36.

Encodings:

BibTeX
V. I. Arnol’d (1986) Catastrophe Theory. 2nd edition, Springer-Verlag, Berlin.

Notes:

Translated from the Russian by G. S. Wassermann, based on a translation by R. K. Thomas. See also Arnol’d (1992).

External Links:

ISBN 3-540-16199-6, MathReview (James Callahan)

Referenced by:

Ch.36.

Encodings:

BibTeX
V. I. Arnol’d (1992) Catastrophe Theory. 3rd edition, Springer-Verlag, Berlin.

Notes:

Translated from the Russian by G. S. Wassermann, Based on a translation by R. K. Thomas

External Links:

ISBN 3-540-54811-4, MathReview (Peter Giblin), ZentralBlatt

Referenced by:

V. I. Arnol’d (1986).

Encodings:

BibTeX
F. M. Arscott and I. M. Khabaza (1962) Tables of Lamé Polynomials. Pergamon Press, The Macmillan Co., New York.

External Links:

MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§29.15(ii), §29.21.

Encodings:

BibTeX
F. M. Arscott (1956) Perturbation solutions of the ellipsoidal wave equation. Quart. J. Math. Oxford Ser. (2) 7, pp. 161–174.

External Links:

ISSN 0033-5606, Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§29.11.

Encodings:

BibTeX
F. M. Arscott (1959) A new treatment of the ellipsoidal wave equation. Proc. London Math. Soc. (3) 9, pp. 21–50.

External Links:

ISSN 0024-6115, Document, MathReview (J. Meixner), ZentralBlatt

Referenced by:

§29.11.

Encodings:

BibTeX
F. M. Arscott (1964a) Integral equations and relations for Lamé functions. Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.

External Links:

Document, MathReview (I. Marx), ZentralBlatt

Referenced by:

§29.8.

Encodings:

BibTeX
F. M. Arscott (1964b) Periodic Differential Equations. An Introduction to Mathieu, Lamé, and Allied Functions. International Series of Monographs in Pure and Applied Mathematics, Vol. 66, Pergamon Press, The Macmillan Co., New York.

External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§28.1, §28.1, §28.10(i), §28.11, §28.12(ii), §28.17, §28.2(ii), §28.2(iii), §28.2(iv), §28.28(i), §28.28(ii), §28.29(i), §28.32(i), §28.32(ii), §28.4(i), §28.5(i), Ch.28, §29.1, §29.11, §29.12(i), §29.12(ii), §29.12(iii), §29.14, §29.15(ii), §29.15(ii), §29.17(i), §29.18(iii), Ch.29, §30.1, §30.10, §30.11(i), §30.11(vi), §30.2(ii), §30.4(iii), §30.6, §30.8(i), §30.8(ii), Ch.30, §31.4, §31.5, §31.9(ii), Notations F, Notations G, Notations M, Notations N.

Encodings:

BibTeX
F. M. Arscott (1967) The Whittaker-Hill equation and the wave equation in paraboloidal co-ordinates. Proc. Roy. Soc. Edinburgh Sect. A 67, pp. 265–276.

External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§28.31(i), §28.31(ii), §28.31(ii), §28.32(ii).

Encodings:

BibTeX
G. Arutyunov and M. Staudacher (2004) Matching higher conserved charges for strings and spins. J. High Energy Phys. 2004 (3).

Notes:

(electronic only, article id. JHEP03(2004)004, 32 pp.).

External Links:

ISSN 1126-6708, Document, MathReview

Referenced by:

§19.35(ii).

Encodings:

BibTeX
U. M. Ascher, R. M. M. Mattheij and R. D. Russell (1995) Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics, Vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

Notes:

Corrected reprint of the 1988 original

External Links:

ISBN 0-89871-354-4, MathReview, ZentralBlatt

Referenced by:

§3.7(iii).

Encodings:

BibTeX
U. M. Ascher and L. R. Petzold (1998) Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

External Links:

ISBN 0-89871-412-5, MathReview (Michael Hanke), ZentralBlatt

Referenced by:

§3.7(i).

Encodings:

BibTeX
N. W. Ashcroft and N. D. Mermin (1976) Solid State Physics. Holt, Rinehart and Winston, New York.

External Links:

ISBN 0-03-083993-9

Referenced by:

§4.44, §8.22(ii).

Encodings:

BibTeX
R. A. Askey, T. H. Koornwinder and W. Schempp (Eds.) (1984) Special Functions: Group Theoretical Aspects and Applications. D. Reidel Publishing Co., Dordrecht.

Notes:

Reprinted by Kluwer Academic Publishers, Boston, 2001.

External Links:

ISBN 90-277-1822-9; 1-4020-0319-6, MathReview, ZentralBlatt

Referenced by:

Profile Tom H. Koornwinder.

Encodings:

BibTeX
R. Askey and J. Fitch (1969) Integral representations for Jacobi polynomials and some applications.. J. Math. Anal. Appl. 26 (2), pp. 411–437.

External Links:

Document, MathReview (D. L. Colton), ZentralBlatt

Referenced by:

§18.17(iv).

Encodings:

BibTeX
R. Askey and G. Gasper (1976) Positive Jacobi polynomial sums. II. Amer. J. Math. 98 (3), pp. 709–737.

External Links:

FullText, MathReview (F. Schipp), ZentralBlatt

Referenced by:

§16.23(iii).

Encodings:

BibTeX
R. Askey and M. E. H. Ismail (1984) Recurrence relations, continued fractions, and orthogonal polynomials. Mem. Amer. Math. Soc. 49 (300), pp. iv+108.

External Links:

ISSN 0065-9266, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§18.28(iv).

Encodings:

BibTeX
R. Askey, T. H. Koornwinder and M. Rahman (1986) An integral of products of ultraspherical functions and a $q$ -extension. J. London Math. Soc. (2) 33 (1), pp. 133–148.

External Links:

ISSN 0024-6107, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§10.22(iv), §14.30(ii).

Encodings:

BibTeX
R. Askey and B. Razban (1972) An integral for Jacobi polynomials. Simon Stevin 46, pp. 165–169.

External Links:

MathReview (H. M. Srivastava)

Referenced by:

§18.17(viii).

Encodings:

BibTeX
R. Askey and J. Wilson (1985) Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc. 54 (319), pp. iv+55.

External Links:

ISSN 0065-9266, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.21(ii), §18.22(ii), §18.28(ii), Ch.18.

Encodings:

BibTeX
R. Askey (1974) Jacobi polynomials. I. New proofs of Koornwinder’s Laplace type integral representation and Bateman’s bilinear sum. SIAM J. Math. Anal. 5, pp. 119–124.

External Links:

ISSN 1095-7154, Document, MathReview (R. P. Soni), ZentralBlatt

Referenced by:

§18.18(iv).

Encodings:

BibTeX
R. Askey (1975) Orthogonal Polynomials and Special Functions. CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 21, Society for Industrial and Applied Mathematics, Philadelphia, PA.

External Links:

ISBN 0-89871-018-9, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.10(ii), §18.18(vii), Profile Richard A. Askey.

Encodings:

BibTeX
R. Askey (1980) Some basic hypergeometric extensions of integrals of Selberg and Andrews. SIAM J. Math. Anal. 11 (6), pp. 938–951.

External Links:

ISSN 0036-1410, Document, MathReview (W. A. Al-Salam), ZentralBlatt

Referenced by:

§17.13, §17.13.

Encodings:

BibTeX
R. Askey (1982) Commentary on the Paper “Beiträge zur Theorie der Toeplitzschen Form”. In Gábor Szegő, Collected Papers. Vol. 1, Contemporary Mathematicians, pp. 303–305.

External Links:

ISBN 3-7643-3056-2, MathReview (G. Piranian)

Referenced by:

§18.33(iv), §18.33(v).

Encodings:

BibTeX
R. Askey (1985) Continuous Hahn polynomials. J. Phys. A 18 (16), pp. L1017–L1019.

External Links:

ISSN 0305-4470, FullText, MathReview (T. S. Chihara), ZentralBlatt

Referenced by:

§18.19, §18.20(ii), §18.21(ii).

Encodings:

BibTeX
R. Askey (1989) Continuous $q$ -Hermite Polynomials when $q>1$ . In $q$ -series and Partitions (Minneapolis, MN, 1988), IMA Vol. Math. Appl., Vol. 18, pp. 151–158.

External Links:

MathReview (Walter Van Assche), ZentralBlatt

Referenced by:

§18.28(vii).

Encodings:

BibTeX
R. Askey (1990) Graphs as an Aid to Understanding Special Functions. In Asymptotic and Computational Analysis, R. Wong (Ed.), Lecture Notes in Pure and Appl. Math., Vol. 124, pp. 3–33.

External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§18.14(iii), Figure 18.4.2, Figure 18.4.2.

Encodings:

BibTeX
M. J. Atia, A. Martínez-Finkelshtein, P. Martínez-González and F. Thabet (2014) Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters. J. Math. Anal. Appl. 416 (1), pp. 52–80.

External Links:

ISSN 0022-247X, Document, Link, MathReview (Vivek Sahai), ZentralBlatt

Referenced by:

§18.15(vi), §18.15(vi).

Encodings:

BibTeX
D. Atkinson and P. W. Johnson (1988) Chiral-symmetry breaking in QCD. I. The infrared domain. Phys. Rev. D (3) 37 (8), pp. 2290–2295.

External Links:

ISSN 0556-2821, Document, MathReview

Referenced by:

§15.18.

Encodings:

BibTeX
M. Audin (1999) Spinning Tops: A Course on Integrable Systems. Cambridge Studies in Advanced Mathematics, Vol. 51, Cambridge University Press, Cambridge.

External Links:

ISBN 0-521-56129-9; 0-521-77919-7, MathReview (Emma Previato), ZentralBlatt

Referenced by:

§22.19(iv).

Encodings:

BibTeX
Axiom (free interactive system) Center for Algorithms and Interactive Scientific Software.

Notes:

Symbolic and extended-precision general purpose computer algebra system.

Referenced by:

§ Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index, § Software Cross Index.

Encodings:

BibTeX
M. Aymar, C. H. Greene and E. Luc-Koenig (1996) Multichannel Rydberg spectroscopy of complex atoms. Reviews of Modern Physics 68, pp. 1015–1123.

External Links:

Document

Referenced by:

§33.22(ii).

Encodings:

BibTeX