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11: Richard A. Askey

… ►Additional books for which Askey served as author or editor include Orthogonal Polynomials and Special Functions, published by SIAM in 1975, Theory and application of special functions, published by Academic Press in 1975, Special Functions: Group Theoretical Aspects and Applications (with T. …

12: 18.38 Mathematical Applications

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Approximation Theory

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Complex Function Theory

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Random Matrix Theory

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Group Representations

►For group-theoretic interpretations of OP’s see Vilenkin and Klimyk (1991, 1992, 1993). …

13: 32.14 Combinatorics

… ►Let $S_N$ be the group of permutations $𝝅$ of the numbers $1,2,\mathrm{\dots },N$ (§26.2). … ►The distribution function $F(s)$ given by (32.14.2) arises in random matrix theory where it gives the limiting distribution for the normalized largest eigenvalue in the Gaussian Unitary Ensemble of $n\times n$ Hermitian matrices; see Tracy and Widom (1994). … ►See Forrester and Witte (2001, 2002) for other instances of Painlevé equations in random matrix theory.

14: Bibliography N

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The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-66289-8, MathReview (D. R. Heath-Brown), ZentralBlatt

Referenced by:

§27.12.

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Handbuch der Theorie der Gammafunktion. B. G. Teubner, Leipzig (German).

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Notes:

For a reprint with corrections see Nielsen (1965).

External Links:

ZentralBlatt (G. Kowalewski)

Referenced by:

§5.12, Ch.5, §6.10(i), §6.10(i), §7.9, §8.1.

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Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten. Chelsea Publishing Co., New York (German).

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Notes:

Both books are textually unaltered except for correction of errata.

External Links:

MathReview

Referenced by:

N. Nielsen (1906a), N. Nielsen (1906b).

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Affine Weyl groups, discrete dynamical systems and Painlevé equations. Comm. Math. Phys. 199 (2), pp. 281–295.

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External Links:

ISSN 0010-3616, Document, MathReview (Alexander Vladimirovich Kitaev), ZentralBlatt

Referenced by:

§32.2(v).

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Notes:

References and links to software for factorization and primality testing.

External Links:

Home Page

Referenced by:

6th item.

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15: Bibliography Z

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The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.

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External Links:

MathReview (J. Browkin), ZentralBlatt

Referenced by:

§25.12(i).

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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications. Dover, New York.

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Notes:

Reprint of 1965 McGraw-Hill Publication

External Links:

ISBN 0-486-65479-6, MathReview Entry

Referenced by:

§1.16(ix).

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On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval. J. Approx. Theory 94 (1), pp. 73–106.

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External Links:

ISSN 0021-9045, Link, MathReview (T. S. Chihara), ZentralBlatt

Referenced by:

§18.33(iii).

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Generalized Watson Transforms and Applications to Group Representations. Ph.D. Thesis, University of Vermont, Burlington,VT.

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Referenced by:

§35.7(ii).

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16: Bibliography H

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

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External Links:

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

Referenced by:

§1.18(x).

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Lie groups, Lie algebras, and representations. Second edition, Graduate Texts in Mathematics, Vol. 222, Springer, Cham.

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Notes:

An elementary introduction

External Links:

ISBN 978-3-319-13466-6; 978-3-319-13467-3, Document, Link, MathReview Entry

Referenced by:

§1.2(vi).

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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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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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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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17: Bibliography K

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The group $\mathrm{O}(4)$, separation of variables and the hydrogen atom. SIAM J. Appl. Math. 30 (4), pp. 630–664.

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External Links:

Document, MathReview (Anthony J. Bracken), ZentralBlatt

Referenced by:

§31.17(i).

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Quantum Groups. Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York.

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External Links:

ISBN 0-387-94370-6, MathReview (Yu. N. Bespalov), ZentralBlatt

Referenced by:

§17.17.

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Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups. In Special Functions: Group Theoretical Aspects and Applications, pp. 1–85.

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Notes:

Reprinted by Kluwer Academic Publishers, Boston, 2002.

External Links:

ISBN 90-277-1822-9; 1-4020-0319-6, MathReview (Jacques Faraut), ZentralBlatt

Referenced by:

§14.31(ii), §15.17(iii), §15.9(ii).

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Askey-Wilson polynomials as zonal spherical functions on the $\mathrm{SU}(2)$ quantum group. SIAM J. Math. Anal. 24 (3), pp. 795–813.

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External Links:

ISSN 0036-1410, Document, Link, MathReview Entry

Referenced by:

(18.28.27).

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Compact quantum groups and $q$-special functions. In Representations of Lie Groups and Quantum Groups, Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.

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Notes:

Sections 3 and 4 also available as arXiv:math/9403216

External Links:

MathReview (Eric M. Opdam)

Referenced by:

(18.27.14_3).

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18: Morris Newman

… ►Newman wrote the book Matrix Representations of Groups, published by the National Bureau of Standards in 1968, and the book Integral Matrices, published by Academic Press in 1972, which became a classic. … ►He served as Associate Editor for Combinatorics and Number Theory for the DLMF project. …

19: 27.5 Inversion Formulas

… ►The set of all number-theoretic functions $f$ with $f(1)\ne 0$ forms an abelian group under Dirichlet multiplication, with the function $\lfloor 1/n\rfloor$ in (27.2.5) as identity element; see Apostol (1976, p. 129). The multiplicative functions are a subgroup of this group. … ►Special cases of Möbius inversion pairs are: … ►Other types of Möbius inversion formulas include: … ►For a general theory of Möbius inversion with applications to combinatorial theory see Rota (1964). …

20: Philip J. Davis

… ►Davis joined the Section as part of a distinguished group of researchers studying mathematical methods for exploiting the new computational power. … ►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. …