spectrum of a self-adjoint extension of a linear differential operator

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11: Bibliography S

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Operators with Singular Continuous Spectrum: I. General Operators. Annals of Mathematics 141 (1), pp. 131–145.

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MathReview Entry

Referenced by:

§1.18(vii).

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Liouville-Green approximations for a class of linear oscillatory difference equations of the second order. J. Comput. Appl. Math. 41 (1-2), pp. 105–116.

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ISSN 0377-0427, Document, MathReview (Wan Biao Ma), ZentralBlatt

Referenced by:

§2.9(iii).

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A Survey on the Liouville-Green (WKB) Approximation for Linear Difference Equations of the Second Order. In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.), pp. 567–577.

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MathReview, ZentralBlatt

Referenced by:

§2.9(iii).

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A stable quotient-difference algorithm. Math. Comp. 34 (150), pp. 515–519.

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ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§3.10(ii).

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An extension of Airy’s equation. SIAM J. Appl. Math. 15 (6), pp. 1400–1412.

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

Referenced by:

(9.13.1), (9.13.10), (9.13.11), (9.13.12), (9.13.2), (9.13.3), (9.13.4), (9.13.5), (9.13.6), (9.13.7), (9.13.8), (9.13.9), §9.13(i), §9.13(i).

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12: Bibliography F

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Asymptotics of the spectrum of the Heun equation and of Heun functions. Izv. Akad. Nauk SSSR Ser. Mat. 55 (3), pp. 631–646 (Russian).

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Notes:

In Russian. English translation: Math. USSR-Izv., 38(1992), no. 3, pp. 621–635 (1992)

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ISSN 0373-2436, Document, MathReview (Andreĭ Bolibrukh), ZentralBlatt

Referenced by:

§31.13.

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A note on the asymptotic expansion of a ratio of gamma functions. Proc. Edinburgh Math. Soc. (2) 15, pp. 43–45.

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ISSN 0013-0915, Document, Link, MathReview (H. A. Lauwerier), ZentralBlatt

Referenced by:

(5.11.14), §5.11(iii), Erratum (V1.0.21) for Equation (5.11.14).

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Uniform asymptotic expansions of a class of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.

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ISSN 0036-1410, Document, MathReview (Roop N. Kesarwani), ZentralBlatt

Referenced by:

§16.22.

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Monodromy- and spectrum-preserving deformations. I. Comm. Math. Phys. 76 (1), pp. 65–116.

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ISSN 0010-3616, Link, MathReview (Hélène Airault), ZentralBlatt

Referenced by:

§32.10(ii), §32.4(iii), §32.8(ii).

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Discrete Painlevé equations and their appearance in quantum gravity. Comm. Math. Phys. 142 (2), pp. 313–344.

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ISSN 0010-3616, Link, MathReview (Nikolai A. Kostov), ZentralBlatt

Referenced by:

§32.15.

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13: 18.38 Mathematical Applications

… ►Linear ordinary differential equations can be solved directly in series of Chebyshev polynomials (or other OP’s) by a method originated by Clenshaw (1957). … ►A symmetric Laurent polynomial is a function of the form …A further operator, the so-called Casimir operator … ►has a solution … ►A review is Milson (2017). …

14: 17.16 Mathematical Applications

… ►Many special cases of $q$-series arise in the theory of partitions, a topic treated in §§27.14(i) and 26.9. In Lie algebras Lepowsky and Milne (1978) and Lepowsky and Wilson (1982) laid foundations for extensive interaction with $q$-series. …

15: Bibliography K

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A proof of Askey’s conjectured $q$-analogue of Selberg’s integral and a conjecture of Morris. SIAM J. Math. Anal. 19 (4), pp. 969–986.

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ISSN 0036-1410, Document, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.13.

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Quasi-linear Stokes phenomenon for the Painlevé first equation. J. Phys. A 37 (46), pp. 11149–11167.

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ISSN 0305-4470, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§32.12(i).

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Heat conduction and diffusion in a fluid medium with a periodic flow. I. Determination of the wave transfer coefficient in a tube, slot, and canal. Akad. Nauk SSSR. Žurnal Eksper. Teoret. Fiz. 21, pp. 964–978.

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External Links:

MathReview (N. A. Hall)

Referenced by:

§10.73(v).

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An extension of Saalschütz’s summation theorem for the series ${}_{r+3}{}^{}F_{r+2}^{}$ . Integral Transforms Spec. Funct. 24 (11), pp. 916–921.

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ISSN 1065-2469, Document, FullText, MathReview (Christian Lavault), ZentralBlatt

Referenced by:

§16.4(ii), §16.4(ii).

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A new proof of a Paley-Wiener type theorem for the Jacobi transform. Ark. Mat. 13, pp. 145–159.

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Document, MathReview (G. Gasper), ZentralBlatt

Referenced by:

§18.10(i).

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16: Jim Pitman

… ► 1949 in Tasmania) is a professor in the departments of statistics and mathematics at the University of California, Berkeley. …Pitman holds a B. …in statistics from the Australian National University, Canberra, and a Ph. … ►He has published extensively on probability, stochastic processes, combinatorics and is a champion for open access to resources in mathematics. ►In November 2015, Pitman was named a Senior Associate Editor of the DLMF.

17: Bibliography G

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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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Document, Code, ZentralBlatt

Referenced by:

2nd item.

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Computing the zeros and turning points of solutions of second order homogeneous linear ODEs. SIAM J. Numer. Anal. 41 (3), pp. 827–855.

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External Links:

ISSN 0036-1429, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vi), §3.8(v).

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Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials. J. Phys. A 47 (1), pp. 015203, 26 pp..

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ISSN 1751-8113, Document, Link, MathReview (Brian Simanek)

Referenced by:

§18.36(vi), §18.36(vi).

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A table of partitions. Proc. London Math. Soc. (2) 39, pp. 142–149.

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Document, ZentralBlatt

Referenced by:

§27.21.

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A table of partitions (II). Proc. London Math. Soc. (2) 42, pp. 546–549.

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Document, ZentralBlatt

Referenced by:

§27.21.

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18: 2.7 Differential Equations

… ►Thus a regular singularity has rank 0. … ►Formal solutions are … ►For extensions to higher-order differential equations see Stenger (1966a, b), Olver (1997a, 1999), and Olde Daalhuis and Olver (1998). … ►Then in $(a_1,a_2)$ the differential equation … ►In a neighborhood, or sectorial neighborhood of a singularity, one member has to be recessive. …

19: 4.46 Tables

… ►Extensive numerical tables of all the elementary functions for real values of their arguments appear in Abramowitz and Stegun (1964, Chapter 4). … ►For 10S values of the first five complex roots of $\sin z=az$, $\cos z=az$, and $\cosh z=az$, for selected positive values of $a$, see Fettis (1976). …

20: Tom H. Koornwinder

… ►During 1968–1992 he was a Researcher in the Centrum Wiskunde & Informatica (CWI), Amsterdam. ►Koornwinder has published numerous papers on special functions, harmonic analysis, Lie groups, quantum groups, computer algebra, and their interrelations, including an interpretation of Askey–Wilson polynomials on quantum SU(2), and a five-parameter extension (the Macdonald–Koornwinder polynomials) of Macdonald’s polynomials for root systems BC. … A. … ►Koornwinder served as a Validator for the original release and publication in May 2010 of the NIST Digital Library of Mathematical Functions and the NIST Handbook of Mathematical Functions. …