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11: Barry I. Schneider

… ► 1940 in Brooklyn, New York) is a staff member of the NIST Applied and Computational Mathematics Division. … ►Schneider’s current research interests span a broad number of areas of theoretical chemistry, atomic and molecular physics, numerical methods and high performance computing. …Schneider has served as Chair and Co-Chair of the APS Division of Computational Physics and the Topical Group on Few-Body Systems and Multipartical Dynamics and has been the organizer of a number of conferences and invited sessions here and abroad. …

12: Bibliography H

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Elliptic Integrals. Dover Publications Inc., New York.

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Notes:

Unaltered reprint of original edition published by Wiley, New York, 1917.

External Links:

MathReview Entry, ZentralBlatt

Referenced by:

§19.8(ii).

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An Introduction to the Theory of Numbers. 5th edition, The Clarendon Press Oxford University Press, New York-Oxford.

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External Links:

ISBN 0-19-853170-2; 0-19-853171-0, MathReview (T. M. Apostol), ZentralBlatt

Referenced by:

§20.12(i), Ch.27.

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Introduction to Numerical Analysis. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:

Reprinted by Dover Publications Inc., New York, 1987.

External Links:

ISBN 0-486-65363-3, MathReview, ZentralBlatt

Referenced by:

§3.3(iii), §3.3(iv), §3.3(v), §3.4(i), §3.8(v), Ch.3.

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Ordinary Differential Equations in the Complex Domain. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.

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Notes:

Reprinted by Dover Publications Inc., New York, 1997

External Links:

ISBN 0-471-39964-7, MathReview (S. Strelitz), ZentralBlatt

Referenced by:

§16.8(i), §32.2(i).

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The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, London-New York.

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Notes:

Reprinted by Chelsea Publishing Company, New York, 1955 and 1965.

External Links:

ISBN 0-8284-0104-7, MathReview, ZentralBlatt

Referenced by:

§14.1, §14.11, §14.16(ii), §14.16(iii), §14.20(x), §14.27, §14.27, §14.3(i), §14.3(i), Ch.14, §29.18(iii), Ch.29.

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13: Bibliography E

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Riemann’s Zeta Function. Academic Press, New York-London.

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Notes:

Pure and Applied Mathematics, Vol. 58. Reprinted by Dover Publications Inc., Mineola, NY, 2001.

External Links:

MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.25.

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A Treatise on the Integral Calculus. Vol. 1-2, Chelsea Publishing Co., New York.

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Notes:

Originally published by Macmillan, 1921-1930.

External Links:

ZentralBlatt

Referenced by:

§19.11(i), §19.4(ii).

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Ten Physical Applications of Spectral Zeta Functions. Lecture Notes in Physics. New Series m: Monographs, Vol. 35, Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-60230-5, MathReview (Alfred Actor), ZentralBlatt

Referenced by:

§25.17.

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Asymptotic Expansions. Dover Publications Inc., New York.

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External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

Ch.2.

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A new series representation for $\zeta (3)$ . Amer. Math. Monthly 97 (3), pp. 219–220.

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External Links:

ISSN 0002-9890, FullText, MathReview (Christian Radoux), ZentralBlatt

Referenced by:

(25.8.10).

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14: Guide to Searching the DLMF

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a textual word, a number, or a math symbol.

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any double-quoted sequence of textual words and numbers.

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adj, prec/n, and near/n, where n is any positive natural number.

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$	stands for any number of alphanumeric characters
	(the more conventional * is reserved for the multiplication operator)
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15: Bibliography B

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New tables of Bessel functions of complex argument. Comput. Math. Math. Phys. 37 (12), pp. 1480–1482.

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Notes:

Russian original in Zh. Vychisl. Mat. i Mat. Fiz. 37(1997), no. 12, 1526–1528

External Links:

ZentralBlatt

Referenced by:

§10.75(i).

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New “coherent” states associated with non-compact groups. Comm. Math. Phys. 21 (1), pp. 41–55.

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External Links:

ISSN 0010-3616, MathReview (R. Mirman), ZentralBlatt

Referenced by:

§13.28(iii).

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Uniform approximation: A new concept in wave theory. Science Progress (Oxford) 57, pp. 43–64.

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Referenced by:

§36.14(i), §9.16.

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Pi and the AGM, A Study in Analytic Number Theory and Computational Complexity. Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York.

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External Links:

ISBN 0-471-83138-7, MathReview (H. London), ZentralBlatt

Referenced by:

§19.35(i), §19.5, §19.8(i), §23.20(iv).

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Introduction to Bessel Functions. Dover Publications Inc., New York.

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Notes:

Unaltered republication of the 1938 edition, published by Longmans, Green and Co., London-New York.

External Links:

MathReview, ZentralBlatt

Referenced by:

§10.73(iii).

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16: Tom M. Apostol

… ►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. … ►In 1998, the Mathematical Association of America (MAA) awarded him the annual Trevor Evans Award, presented to authors of an exceptional article that is accessible to undergraduates, for his piece entitled “What Is the Most Surprising Result in Mathematics?” (Answer: the prime number theorem). …In addition, he was the co-author of New Horizons in Geometry, published by the MAA, which received the CHOICE “Outstanding Academic Title” award in 2013. … ►

27 Functions of Number Theory

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17: Bibliography G

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New inequalities for the zeros of Jacobi polynomials. SIAM J. Math. Anal. 18 (6), pp. 1549–1562.

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External Links:

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

Referenced by:

§18.16(ii), §18.16(vi).

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New inequalities for the zeros of confluent hypergeometric functions. In Asymptotic and computational analysis (Winnipeg, MB, 1989), pp. 175–192.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§13.9(i), §13.9(ii).

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DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics. Comput. Phys. Comm. 139 (2), pp. 186–191.

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External Links:

Document, Code, ZentralBlatt

Referenced by:

2nd item.

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A new identity for some six-$j$ symbols. J. Math. Phys. 32 (6), pp. 1430–1432.

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External Links:

ISSN 0022-2488, Document, MathReview

Referenced by:

§34.5(vi).

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Inductance Calculations. Van Nostrand, New York.

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Notes:

Reprinted by Dover, New York, 1962 and 2004

External Links:

ZentralBlatt

Referenced by:

§19.34.

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18: Bibliography P

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Signal Analysis. McGraw-Hill, New York.

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External Links:

ISBN 00-704-8460-0, 00-706-6468-4, ZentralBlatt

Referenced by:

§30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).

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Handbook of the Normal Distribution. Statistics: Textbooks and Monographs, Vol. 40, Marcel Dekker Inc., New York.

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Notes:

A revised and expanded 2nd edition was published in 1996.

External Links:

ISBN 0-8247-1541-1, MathReview (S. Kotz), ZentralBlatt

Referenced by:

§7.20(iii).

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A new basis for the representation of the rotation group. Lamé and Heun polynomials. J. Mathematical Phys. 14 (8), pp. 1130–1139.

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External Links:

Document, ZentralBlatt

Referenced by:

§29.18(iv).

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Ideas of Quantum Chemistry. second edition, Elsevier, Amsterdam-New York.

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External Links:

ISBN 978-0-444-59436-5

Referenced by:

§18.39(ii).

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Numerical Solution of Sturm-Liouville Problems. Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.

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External Links:

ISBN 0-19-853415-9, MathReview (L. Greenberg), ZentralBlatt

Referenced by:

§3.7(iv).

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19: Bibliography T

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New congruences for the Bernoulli numbers. Math. Comp. 48 (177), pp. 341–350.

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External Links:

ISSN 0025-5718, FullText, MathReview (Wells Johnson), ZentralBlatt

Referenced by:

1st item.

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On the computation of the incomplete gamma functions for large values of the parameters. In Algorithms for approximation (Shrivenham, 1985), Inst. Math. Appl. Conf. Ser. New Ser., Vol. 10, pp. 479–489.

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External Links:

FullText, MathReview (G. Meinardus), ZentralBlatt

Referenced by:

§8.25(iii).

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Bernoulli polynomials old and new: Generalizations and asymptotics. CWI Quarterly 8 (1), pp. 47–66.

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External Links:

ISSN 0922-5366, FullText, MathReview (Michael Hauss), ZentralBlatt

Referenced by:

§24.11, §24.16(i).

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Fourier Series. Prentice-Hall Inc., Englewood Cliffs, N.J..

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Notes:

Translated from the Russian by Richard A. Silverman. Second English edition published by Dover Publications Inc., New York, 1976.

External Links:

MathReview (R. P. Boas, Jr.), ZentralBlatt

Referenced by:

§1.8(i), §1.8(ii).

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Applied Combinatorics. 5th edition, John Wiley and Sons, New York.

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Referenced by:

§26.15.

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20: Bibliography O

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Fourier Expansions. A Collection of Formulas. Academic Press, New York-London.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§1.8(v), §22.11, §4.27.

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A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations. Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.

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External Links:

Document, MathReview (J. Todd), ZentralBlatt

Referenced by:

§10.21(ii).

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Some new asymptotic expansions for Bessel functions of large orders. Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.

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External Links:

Document, MathReview (F. Oberhettinger), ZentralBlatt

Referenced by:

§10.19(iii), §10.21(vii).

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Applications of Lie Groups to Differential Equations. 2nd edition, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York.

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External Links:

ISBN 0-387-94007-3; 0-387-95000-1, MathReview, ZentralBlatt

Referenced by:

§32.13(i).

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OEIS Foundation, Inc., Highland Park, New Jersey.

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Notes:

A tool for finding and identifying integer sequences.

External Links:

On-Line Encyclopedia of Integer Sequences

Referenced by:

5th item.

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