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21: 19 Elliptic Integrals

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22: Bibliography S

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Evaluation of associated Legendre functions off the cut and parabolic cylinder functions. Electron. Trans. Numer. Anal. 9, pp. 137–146.

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Notes:

Orthogonal polynomials: numerical and symbolic algorithms (Leganés, 1998)

External Links:

ISSN 1068-9613, FullText, MathReview (Adam Marlewski), ZentralBlatt

Referenced by:

§14.30(i), 3rd item.

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On the expansion of the parabolic cylinder function in a series of the product of two parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 3, pp. 226–230.

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External Links:

ZentralBlatt

Referenced by:

§12.13(i).

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Topics in Complex Function Theory. Vol. III: Abelian Functions and Modular Functions of Several Variables. Interscience Tracts in Pure and Applied Mathematics, No. 25, Wiley-Interscience, [John Wiley & Sons, Inc], New York-London-Sydney.

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Notes:

Translated from the original German by E. Gottschling and M. Tretkoff. Reprinted by John Wiley & Sons, New York, 1989.

External Links:

ISBN 0-471-79090-7, MathReview, ZentralBlatt

Referenced by:

Ch.21.

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Introduction to Riemann Surfaces. Addison-Wesley Publishing Company, Reading, Massachusetts.

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Notes:

A second edition was published in 1981 (Chelsea Publishing Co., New York, and AMS Chelsea Book Series, American Mathematical Society, Providence, Rhode Island)

External Links:

MathReview (L. Sario), ZentralBlatt (H. Wittich)

Referenced by:

§21.7(i).

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Automatic computing methods for special functions. IV. Complex error function, Fresnel integrals, and other related functions. J. Res. Nat. Bur. Standards 86 (6), pp. 661–686.

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Notes:

Includes Fortran code, maximum accuracy 18S.

External Links:

ISSN 0022-4340, MathReview, ZentralBlatt

Referenced by:

§7.25(iii).

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23: Bibliography W

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Evaluating elliptic functions and their inverses. Comput. Math. Appl. 39 (3-4), pp. 131–136.

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External Links:

ISSN 0898-1221, Document, MathReview, ZentralBlatt

Referenced by:

§22.20(ii), §22.20(v).

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Infinitely differentiable generalized logarithmic and exponential functions. Math. Comp. 57 (196), pp. 723–733.

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ISSN 0025-5718, FullText, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§4.12.

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Reduction formulae for products of theta functions. J. Res. Nat. Inst. Standards and Technology 117, pp. 297–303.

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External Links:

Document

Referenced by:

(20.7.34), §20.7(ix).

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Analytic Theory of Continued Fractions. D. Van Nostrand Company, Inc., New York.

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Notes:

Reprinted by Chelsea Publishing, New York, 1973 and AMS Chelsea Publishing, Providence, RI, 2000.

External Links:

ISBN 0-8218-2106-7, MathReview (R. C. Buck), ZentralBlatt

Referenced by:

§3.10(iii), §4.25, §4.9(i), §4.9(ii), Ch.4, §5.10.

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The cubic transformation of the hypergeometric function. Quart. J. Pure and Applied Math. 41, pp. 70–79.

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External Links:

ZentralBlatt

Referenced by:

§15.8(v), §15.8(v).

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24: Bibliography M

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Hypergeometric Functions.

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Notes:

Unpublished Lecture Notes, University of London. An online version exists.

External Links:

FullText

Referenced by:

§35.7(ii), §35.8(iii).

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Contribution no. 14. The Riemann zeta function. BIT 5, pp. 138–141.

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Referenced by:

§25.21(ii).

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Uniform computation of the error function and other related functions. Math. Comp. 25 (114), pp. 339–344.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§7.22(i).

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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.

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External Links:

Document, ZentralBlatt

Referenced by:

§27.13(iv).

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The Calculus of Finite Differences. Macmillan and Co. Ltd., London.

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Notes:

Reprinted in 1951 by Macmillan, and in 1981 by Chelsea Publishing Co., New York, and American Mathematical Society, AMS Chelsea Book Series, Providence, RI.

External Links:

ZentralBlatt

Referenced by:

§24.16(i), §24.17(i), §24.2(i), §24.2(ii), §24.4(i), §24.4(ii), §24.4(iii), §24.4(v), §26.1, §26.1, Notations B, Notations B.

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25: Bibliography R

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On the partition function p(n). Proc. London Math. Soc. (2) 43 (4), pp. 241–254.

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External Links:

Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.14(iii).

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Special Functions. The Macmillan Co., New York.

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External Links:

MathReview (R. Hamming), ZentralBlatt

Referenced by:

§14.7(iv), §16.3(ii), §16.3(ii), §16.4(iii), (18.12.2_5), §18.12, §18.9(ii).

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Collected Papers of Srinivasa Ramanujan. Chelsea Publishing Co., New York.

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Notes:

Reprinted with commentary by Bruce Berndt, AMS Chelsea Publishing Series, American Mathematical Society (2000).

External Links:

ISBN 0-8218-2076-1

Referenced by:

§8.11(v), G. H. Hardy and S. Ramanujan (1918).

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Elliptic Functions, Theta Functions, and Riemann Surfaces. The Williams & Wilkins Co., Baltimore, MD.

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External Links:

MathReview (H. H. Martens), ZentralBlatt

Referenced by:

§20.11(iv), §20.12(ii).

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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).

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External Links:

Link, ISSN 2227-7390, Document

Referenced by:

§8.15.

Encodings:

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26: Bibliography T

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The asymptotic expansion of the incomplete gamma functions. SIAM J. Math. Anal. 10 (4), pp. 757–766.

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External Links:

ISSN 0036-1410, Document, MathReview (E. Riekstiņš), ZentralBlatt

Referenced by:

§8.12.

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Asymptotic inversion of incomplete gamma functions. Math. Comp. 58 (198), pp. 755–764.

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External Links:

ISSN 0025-5718, FullText, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§8.12, §8.12.

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The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions. Report TW 183/78 Mathematisch Centrum, Amsterdam, Afdeling Toegepaste Wiskunde.

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Notes:

Algol procedures, maximum accuracy 14S.

External Links:

FullText, ZentralBlatt

Referenced by:

§12.21(ii).

Encodings:

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Representation Theory and Harmonic Analysis. Contemporary Mathematics, Vol. 191, American Mathematical Society, Providence, RI.

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Notes:

Papers from the conference held in honor of Ray A. Kunze at the AMS Special Session, Cincinnati, Ohio, January 12–14, 1994

External Links:

ISBN 0-8218-0310-7, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

Profile Donald St. P. Richards.

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Special functions in phase space: Mathieu functions. J. Phys. A 31 (31), pp. 6725–6739.

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External Links:

ISSN 0305-4470, Document, MathReview (Bing Hong Wang), ZentralBlatt

Referenced by:

8th item.

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27: Bibliography C

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The hypergeometric function and the $R$-function near their branch points. Rend. Sem. Mat. Univ. Politec. Torino (Special Issue), pp. 63–89.

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Notes:

International conference on special functions: theory and computation (Turin, 1984)

External Links:

ISSN 0373-1243, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§19.27(vi).

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Introduction to Approximation Theory. 2nd edition, Chelsea Publishing Co., New York.

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Notes:

Reprinted by AMS Chelsea Publishing, Providence, RI, 1998

External Links:

ISBN 0-8218-1374-9, MathReview, ZentralBlatt

Referenced by:

§18.38(i).

Encodings:

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Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges. 6th edition, Vol. 1, Chelsea Publishing Co., New York.

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Notes:

A seventh edition (reprinting of the sixth edition) was published by AMS Chelsea Publishing Series, American Mathematical Society, 1964.

External Links:

ISBN 978-0-8218-1648-6, Seventh Edition, MathReview, ZentralBlatt

Referenced by:

§1.2(i), §1.2(ii), §1.2(iii), §1.2(iii).

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Algebra: An Elementary Textbook for the Higher Classes of Secondary Schools and for Colleges. 6th edition, Vol. 2, Chelsea Publishing Co., New York.

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Notes:

A seventh edition (reprinting of the sixth edition) was published by AMS Chelsea Publishing Series, American Mathematical Society, 1964.

External Links:

ISBN 978-0-8218-1649-3, Seventh Edition, MathReview, ZentralBlatt

Referenced by:

§1.2(i).

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A compact mathematical function package. Australian Computer Journal 16 (3), pp. 107–114.

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Notes:

Includes Pascal function evaluation package

External Links:

ISSN 0004-8917, ZentralBlatt

Referenced by:

§16.27(ii).

Encodings:

BibTeX

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28: Bibliography J

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Some properties of the Erlang loss function. Bell System Tech. J. 53, pp. 525–551.

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External Links:

ISSN 0005-8580, MathReview (U. Narayan Bhat), ZentralBlatt

Referenced by:

§8.23.

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Asymptotics of the hypergeometric function. Math. Methods Appl. Sci. 24 (6), pp. 369–389.

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External Links:

ISSN 0170-4214, Document, MathReview, ZentralBlatt

Referenced by:

§14.15(iii), §15.12(iii).

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Parabolic cylinder functions of large order. J. Comput. Appl. Math. 190 (1-2), pp. 453–469.

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External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§12.10(vi).

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Calculus of Finite Differences. Hungarian Agent Eggenberger Book-Shop, Budapest.

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Notes:

Third edition published in 1965 by Chelsea Publishing Co., New York, and American Mathematical Society, AMS Chelsea Book Series, Providence, RI

External Links:

MathReview (W. E. Milne), ZentralBlatt

Referenced by:

§26.1, §26.1, §26.8(vii), §5.16, Notations S.

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Calculus of Finite Differences. 3rd edition, AMS Chelsea, Providence, RI.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§24.17(i), §24.6.

Encodings:

BibTeX

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29: Bibliography K

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On the evaluation of the Gauss hypergeometric function. C. R. Acad. Bulgare Sci. 45 (6), pp. 35–36.

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External Links:

ISSN 0861-1459, MathReview, ZentralBlatt

Referenced by:

§15.15, §15.19(i).

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Generalized functions. Mathematics in Science and Engineering, Vol. 171, Academic Press, Inc., Orlando, FL.

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Notes:

Theory and technique

External Links:

ISBN 0-12-396560-8, MathReview (Qing Yi Chen), ZentralBlatt

Referenced by:

§1.16(viii).

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Complex zeros of an incomplete Riemann zeta function and of the incomplete gamma function. Math. Comp. 24 (111), pp. 679–696.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§8.13(iii), §8.22(ii).

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Programs for computing the logarithm of the gamma function, and the digamma function, for complex argument. Comput. Phys. Comm. 4, pp. 221–226.

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Notes:

Single-precision Fortran, accuracy 12-14S

External Links:

Document, Code

Referenced by:

1st item.

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The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.

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External Links:

MathReview (G. L. Lamb, Jr.), ZentralBlatt

Referenced by:

§22.19(iii).

Encodings:

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