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11: Philip J. Davis

… ►An interesting anecdote told by Davis reveals that he and mathematician Philip Rabinowitz were dubbed “Heroes of the SEAC” when their Gaussian integration code executed correctly on its first run. … ►At CalTech, John Todd dedicated himself to the training of new researchers in numerical analysis, and Olga Taussky, who had been a full-time NBS consultant influential in establishing the field of matrix theory, became the first woman at CalTech to attain the academic rank of full professor. …

12: Bibliography K

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Replica field theories, Painlevé transcendents, and exact correlation functions. Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).

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External Links:

ISSN 0031-9007, Document, MathReview, ZentralBlatt

Referenced by:

§32.16.

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An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives. Computer Physics Comm. 132 (1-2), pp. 142–165.

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Document, Code, ZentralBlatt

Referenced by:

§36.15(iii).

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Neue Untersuchungen einer Reihe aus der Theorie der elliptischen Funktionen. Journal für die Reine und Angenwandte Mathematik 158, pp. 209–218 (German).

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ZentralBlatt

Referenced by:

§19.5.

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Theorie und Anwendung der unendlichen Reihen. 4th edition, Die Grundlehren der mathematischen Wissenschaften, Band 2, Springer-Verlag, Berlin-Heidelberg (German).

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Notes:

A translation by R. C. Young appeared in 1928, Theory and Application of Infinite Series, Blackie, 571pp.

External Links:

MathReview, ZentralBlatt

Referenced by:

§3.9(ii).

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Zur Theorie der Modulformen $n$-ten Grades. I. Math. Z. 59, pp. 399–416 (German).

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ISSN 0025-5874, Document, MathReview (H. S. Zuckerman), ZentralBlatt

Referenced by:

§35.6(i).

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13: Bibliography F

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Algorithms and codes for the Macdonald function: Recent progress and comparisons. J. Comput. Appl. Math. 161 (1), pp. 179–192.

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External Links:

ISSN 0377-0427, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.77(vi).

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Algorithm 838: Airy functions. ACM Trans. Math. Software 30 (4), pp. 491–501.

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Notes:

Single- and double-precision Fortran, maximum accuracy 32S.

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ISSN 0098-3500, Document, Code, MathReview Entry, ZentralBlatt

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3rd item, 2nd item, 1st item.

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A computer program for the calculation of angular-momentum coupling coefficients. Comput. Phys. Comm. 70 (1), pp. 147–153.

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Notes:

Fortran for exact calculation using integers

External Links:

ISSN 0010-4655, Document, Code, MathReview Entry

Referenced by:

§34.13, §34.13, 5th item.

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Computing the hypergeometric function. J. Comput. Phys. 137 (1), pp. 79–100.

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Notes:

Double-precision Fortran

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ISSN 0021-9991, Document, Code, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

§15.19(i), 1st item, 2nd item.

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Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond. In Recent Perspectives in Random Matrix Theory and Number Theory, London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§18.38(ii).

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14: Bibliography P

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Algorithm 385: Exponential integral $\mathrm{Ei}(x)$ . Comm. ACM 13 (7), pp. 446–447.

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Notes:

Includes Fortran code, maximum accuracy 20D. For certification and remarks see same journal v. 13 (1970), pp. 448–449 and p. 750; v. 15 (1972), p. 1074.

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ISSN 0001-0782, Document

Referenced by:

§6.21(ii).

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Statistical Field Theory. Addison-Wesley, Reading, MA.

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External Links:

ISBN 0-201-05985-1, MathReview (Tony C. Dorlas), ZentralBlatt

Referenced by:

§22.19(ii).

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Notes:

Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

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6th item.

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Gauge Field Theories. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.

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ISBN 0-521-26537-1, MathReview (G. R. Allcock), ZentralBlatt

Referenced by:

§22.19(ii).

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Catastrophe Theory and its Applications. Pitman, London.

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Notes:

Reprinted by Dover in 1996.

External Links:

ISBN 0-273-01029-8, MathReview (George K. Francis), ZentralBlatt

Referenced by:

§36.4(i), Ch.36.

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15: Bibliography H

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Quantum theory for mathematicians. Graduate Texts in Mathematics, Vol. 267, Springer, New York.

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ISBN 978-1-4614-7115-8; 978-1-4614-7116-5, Document, Link, MathReview Entry

Referenced by:

§1.18(x).

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Molecular Electronic-Structure Theory. John Wiley & Sons, New York.

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Notes:

Paperback Reprint of 2004 Edition

External Links:

ISBN 9871118531471

Referenced by:

§18.39(iii).

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Algorithm AS66: The normal integral. Appl. Statist. 22 (3), pp. 424–427.

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Notes:

Double-precision Fortran, maximum accuracy 12D.

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FullText, Code

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5th item.

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Two-center Coulomb functions. Comput. Phys. Comm. 103 (2-3), pp. 209–216.

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Notes:

Double-precision Fortran code.

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ISSN 0010-4655, Document, Code

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6th item.

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Development of a Gaussian hypergeometric function code in complex domains. Internat. J. Modern Phys. C 4 (4), pp. 805–840.

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ISSN 0129-1831, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§15.20(iii).

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16: Bibliography M

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The Theory of Groups. Clarendon Press, Oxford.

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Notes:

Reprinted in 1988 by Krieger Publishing Co., Malabar, FL

External Links:

ISBN 0-19-853137-0;0-89464-287-1, MathReview (A. P. Street), ZentralBlatt

Referenced by:

§23.20(ii).

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Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function. Appl. Statist. 38 (2), pp. 397–402.

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FullText, Code, ZentralBlatt

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5th item.

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Zur Theorie des zylindrisch-parabolischen Spiegels. Z. Physik 118, pp. 343–356 (German).

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External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§12.17.

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Loud Speakers: Theory, Performance, Testing and Design. Oxford University Press, New York.

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Notes:

Reprinted, with corrections, by Dover Publications Inc., 1960.

External Links:

MathReview, ZentralBlatt

Referenced by:

§11.12.

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Precise Coulomb wave functions for a wide range of complex $\mathrm{\ell }$, $\eta$ and $z$ . Computer Physics Communications 176 (3), pp. 232–249.

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Notes:

C++ code. Maximum accuracy 10D

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

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17: Bibliography D

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Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.

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Notes:

Revised and with a preface by Hugh L. Montgomery

External Links:

ISBN 0-387-95097-4, MathReview, ZentralBlatt

Referenced by:

§27.12.

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Pólya’s Theory of Counting. In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.), pp. 144–184.

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External Links:

ISBN 0898741726

Referenced by:

§26.20.

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Computing Riemann theta functions. Math. Comp. 73 (247), pp. 1417–1442.

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Notes:

Two of the authors (Deconinck and van Hoeij) have developed Maple code for the algorithms described in this paper.

External Links:

ISSN 0025-5718, Document, Code, MathReview, ZentralBlatt

Referenced by:

§21.10(i), 1st item, §21.2(i), §21.4, M. Heil (1995).

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Elements of the Theory of Numbers. Harcourt/Academic Press, San Diego, CA.

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External Links:

ISBN 0-12-209130-2, MathReview (Bruce C. Berndt), ZentralBlatt

Referenced by:

Ch.24.

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A fast new public code for computing photon orbits in a Kerr spacetime. The Astrophysical Journal 696, pp. 1616–1629.

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External Links:

Document

Referenced by:

§19.35(ii).

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18: Bibliography L

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Exact computation of the $9$-$j$ symbols. Comput. Phys. Comm. 70 (3), pp. 544–556.

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Notes:

Double-precision Fortran

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ISSN 0010-4655, Document, Code, MathReview

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7th item.

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Essai sur la Théorie des Nombres. 2nd edition, Courcier, Paris.

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External Links:

ZentralBlatt

Referenced by:

§27.2(i).

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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions. Comput. Phys. Comm. 99 (2-3), pp. 297–306.

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Notes:

Single-precision Fortran, maximum accuracy 8S.

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ISSN 0010-4655, Document, Code, ZentralBlatt

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4th item.

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Zur Theorie der Gaußschen Summen. Math. Ann. 57 (4), pp. 554–567 (German).

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External Links:

ISSN 0025-5831, Document, MathReview Entry, ZentralBlatt

Referenced by:

§20.11(i).

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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions. third edition, Springer, New York.

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External Links:

ISBN 0387955518

Referenced by:

§18.39(iii).

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19: Software Index

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	Open Source													With Book						Commercial
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27 Functions of Number Theory
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This is software of narrow scope developed as a byproduct of a research project and subsequently made available at no cost to the public. The software is often meant to demonstrate new numerical methods or software engineering strategies which were the subject of a research project. When developed, the software typically contains capabilities unavailable elsewhere. While the software may be quite capable, it is typically not professionally packaged and its use may require some expertise. The software is typically provided as source code or via a web-based service, and no support is provided.

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These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

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20: Bibliography R

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Topics in Analytic Number Theory. Springer-Verlag, New York.

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Notes:

Edited by E. Grosswald, J. Lehner and M. Newman, Die Grundlehren der mathematischen Wissenschaften, Band 169

External Links:

MathReview (H. Halberstam), ZentralBlatt

Referenced by:

§1.8(iv), §20.7(viii), §20.7(viii), Ch.24.

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A code to calculate (high order) Bessel functions based on the continued fractions method. Comput. Phys. Comm. 76 (3), pp. 381–388.

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Notes:

Double-precision Fortran, maximum accuracy 18D.

External Links:

ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt

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6th item.

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Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse. Inauguraldissertation, Göttingen.

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Referenced by:

§21.7(i).

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Elementary Number Theory and its Applications. 5th edition, Addison-Wesley, Reading, MA.

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External Links:

ISBN 0-201-87073-8, MathReview (Norman J. Richert)

Referenced by:

§27.17.

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On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, pp. 340–368.

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External Links:

Document, MathReview (M. A. Harrison), ZentralBlatt

Referenced by:

§27.5.

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