DLMF: Untitled Document

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C. L. Frenzen and R. Wong (1985b) A uniform asymptotic expansion of the Jacobi polynomials with error bounds. Canad. J. Math. 37 (5), pp. 979–1007.

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External Links:: ISSN 0008-414X, MathReview (R. A. Askey), ZentralBlatt
Referenced by:: §18.15(i), §18.16(ii).
Encodings:: BibTeX

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Ultraspherical

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Legendre

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Jacobi

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Ultraspherical

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Laguerre

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Chapter 18 Orthogonal Polynomials

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§18.22(i) Recurrence Relations in $n$

… ►These polynomials satisfy (18.22.2) with

p_{n}(x)

,

A_{n}

, and

C_{n}

as in Table 18.22.1. ►

Table 18.22.1: Recurrence relations (18.22.2) for Krawtchouk, Meixner, and Charlier polynomials.

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$p_{n}(x)$	$A_{n}$	$C_{n}$
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§18.22(ii) Difference Equations in $x$

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§18.22(iii) $x$ -Differences

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H. Delange (1988) On the real roots of Euler polynomials. Monatsh. Math. 106 (2), pp. 115–138.

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External Links:: ISSN 0026-9255, MathReview (H. M. Srivastava), ZentralBlatt
Referenced by:: §24.12(ii).
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K. Dilcher (2008) On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.

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External Links:: ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt
Referenced by:: §24.12(iv).
Encodings:: BibTeX

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G. C. Donovan, J. S. Geronimo, and D. P. Hardin (1999) Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. SIAM J. Math. Anal. 30 (5), pp. 1029–1056.

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External Links:: ISSN 0036-1410, Document, MathReview (Kathi Karima Selig), ZentralBlatt
Referenced by:: §16.4(iii).
Encodings:: BibTeX

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T. M. Dunster (2001b) Uniform asymptotic expansions for Charlier polynomials. J. Approx. Theory 112 (1), pp. 93–133.

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External Links:: ISSN 0021-9045, Document, MathReview (Eberhard Wagner), ZentralBlatt
Referenced by:: §18.24.
Encodings:: BibTeX

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L. Durand (1975) Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics. In Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), R. A. Askey (Ed.), pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.

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External Links:: MathReview (K. M. Saksena), ZentralBlatt
Referenced by:: (12.12.4), §12.12, §18.17(iii), §18.17(iii).
Encodings:: BibTeX

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D. J. Leeming (1989) The real zeros of the Bernoulli polynomials. J. Approx. Theory 58 (2), pp. 124–150.

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External Links:: ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt
Referenced by:: §24.12(i), §24.9.
Encodings:: BibTeX

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D. H. Lehmer (1940) On the maxima and minima of Bernoulli polynomials. Amer. Math. Monthly 47 (8), pp. 533–538.

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External Links:: FullText, MathReview (W. E. Milne), ZentralBlatt
Referenced by:: §24.12(i), §24.9.
Encodings:: BibTeX

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J. L. López and N. M. Temme (1999a) Approximation of orthogonal polynomials in terms of Hermite polynomials. Methods Appl. Anal. 6 (2), pp. 131–146.

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External Links:: ISSN 1073-2772, Pdf, MathReview, ZentralBlatt
Referenced by:: §18.15(vi), §18.16(vi).
Encodings:: BibTeX

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J. L. López and N. M. Temme (1999b) Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials. J. Math. Anal. Appl. 239 (2), pp. 457–477.

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External Links:: ISSN 0022-247X, Document, MathReview (A. G. Law), ZentralBlatt
Referenced by:: §18.34(iii), §24.11, §24.16(i), §24.16(i).
Encodings:: BibTeX

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J. L. López (1999) Asymptotic expansions of the Whittaker functions for large order parameter. Methods Appl. Anal. 6 (2), pp. 249–256.

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Notes:: Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part II
External Links:: ISSN 1073-2772, Pdf, MathReview, ZentralBlatt
Referenced by:: §13.21(i), §13.24(ii).
Encodings:: BibTeX

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I. M. Sheffer (1939) Some properties of polynomial sets of type zero. Duke Math. J. 5, pp. 590–622.

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External Links:: ISSN 0012-7094, Link, MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §18.2(xii).
Encodings:: BibTeX

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A. Sri Ranga (2010) Szegő polynomials from hypergeometric functions. Proc. Amer. Math. Soc. 138 (12), pp. 4259–4270.

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External Links:: ISSN 0002-9939, Link, MathReview (Andrei Martínez Finkelshtein), ZentralBlatt
Referenced by:: §18.33(iv).
Encodings:: BibTeX

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W. F. Sun (1996) Uniform asymptotic expansions of Hermite polynomials. M. Phil. thesis, City University of Hong Kong.

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External Links:: Abstract
Referenced by:: §18.16(v).
Encodings:: BibTeX

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R. F. Swarttouw (1997) A computer implementation of the Askey-Wilson scheme. Technical Report 13 Vrije Universteit Amsterdam.

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External Links:: FullText
Referenced by:: CAOP (website).
Encodings:: BibTeX

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O. Szász (1950) On the relative extrema of ultraspherical polynomials. Boll. Un. Mat. Ital. (3) 5, pp. 125–127.

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External Links:: MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §18.14(iii).
Encodings:: BibTeX

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G. Gasper and M. Rahman (2004) Basic Hypergeometric Series. Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.

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Notes:: With a foreword by Richard Askey
External Links:: ISBN 0-521-83357-4, MathReview (Shaun Cooper), ZentralBlatt
Referenced by:: §17.1, §17.1, §17.10, (17.11.1), (17.11.2), (17.11.3), §17.13, §17.16, (17.4.5), (17.4.6), (17.4.7), (17.4.8), §17.4(i), §17.5, §17.6(i), §17.6(ii), §17.6(iii), §17.6(iv), §17.6(v), §17.7(i), §17.7(ii), §17.7(iii), §17.8, (17.9.3), §17.9(i), §17.9(ii), §17.9(iii), Ch.17, §18.27(i), §18.27(i), §18.27(ii), §18.27(iii), §18.27(iv), (18.28.24), (18.28.25), §18.28(i), §18.28(ii), §18.28(v), §18.28(viii), §26.19, Erratum (V1.0.10) for Section 17.1, Erratum (V1.0.23) for Equation (17.9.3).
Encodings:: BibTeX

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G. Gasper (1972) An inequality of Turán type for Jacobi polynomials. Proc. Amer. Math. Soc. 32, pp. 435–439.

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External Links:: ISSN 0002-9939, Document, MathReview (A. E. Danese), ZentralBlatt
Referenced by:: §18.14(ii).
Encodings:: BibTeX

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W. Gautschi (1975) Computational Methods in Special Functions – A Survey. In Theory and Application of Special Functions (Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975), R. A. Askey (Ed.), pp. 1–98. Math. Res. Center, Univ. Wisconsin Publ., No. 35.

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External Links:: MathReview (H. E. Fettis), ZentralBlatt
Referenced by:: §19.36(ii), §19.5.
Encodings:: BibTeX

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W. Gautschi (1984) Questions of Numerical Condition Related to Polynomials. In Studies in Numerical Analysis, G. H. Golub (Ed.), pp. 140–177.

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External Links:: MathReview Entry, ZentralBlatt
Referenced by:: §3.8(vi).
Encodings:: BibTeX

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V. X. Genest, L. Vinet, and A. Zhedanov (2016) The non-symmetric Wilson polynomials are the Bannai-Ito polynomials. Proc. Amer. Math. Soc. 144 (12), pp. 5217–5226.

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External Links:: ISSN 0002-9939, Link, MathReview (Raj Wilson), ZentralBlatt
Referenced by:: §18.28(xi).
Encodings:: BibTeX

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L. Habsieger (1988) Une

q

-intégrale de Selberg et Askey. SIAM J. Math. Anal. 19 (6), pp. 1475–1489.

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External Links:: ISSN 0036-1410, Document, MathReview (R. A. Askey), ZentralBlatt
Referenced by:: §17.13.
Encodings:: BibTeX

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E. Hahn (1980) Asymptotik bei Jacobi-Polynomen und Jacobi-Funktionen. Math. Z. 171 (3), pp. 201–226 (German).

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External Links:: ISSN 0025-5874, Document, MathReview (R. A. Askey), ZentralBlatt
Referenced by:: §18.15(i).
Encodings:: BibTeX

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B. A. Hargrave and B. D. Sleeman (1977) Lamé polynomials of large order. SIAM J. Math. Anal. 8 (5), pp. 800–842.

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External Links:: Document, MathReview (F. M. Arscott), ZentralBlatt
Referenced by:: §29.16.
Encodings:: BibTeX

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E. Hendriksen and H. van Rossum (1986) Orthogonal Laurent polynomials. Nederl. Akad. Wetensch. Indag. Math. 48 (1), pp. 17–36.

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External Links:: ISSN 0019-3577, Document, MathReview (W. J. Thron), ZentralBlatt
Referenced by:: §18.33(v).
Encodings:: BibTeX

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F. T. Howard (1976) Roots of the Euler polynomials. Pacific J. Math. 64 (1), pp. 181–191.

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External Links:: MathReview (M. Marden), ZentralBlatt
Referenced by:: §24.12(ii).
Encodings:: BibTeX

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Askey polynomials

31—40 of 44 matching pages

31: 1 Algebraic and Analytic Methods

32: Bibliography F

33: 18.10 Integral Representations

Ultraspherical

Legendre

Jacobi

Ultraspherical

Laguerre

34: 18 Orthogonal Polynomials

Chapter 18 Orthogonal Polynomials

35: 18.22 Hahn Class: Recurrence Relations and Differences

§18.22(i) Recurrence Relations in $n$

§18.22(ii) Difference Equations in $x$

§18.22(iii) $x$ -Differences

36: Bibliography D

37: Bibliography L

38: Bibliography S

39: Bibliography G

40: Bibliography H

Askey polynomials

31—40 of 44 matching pages

31: 1 Algebraic and Analytic Methods

32: Bibliography F

33: 18.10 Integral Representations

Ultraspherical

Legendre

Jacobi

Ultraspherical

Laguerre

34: 18 Orthogonal Polynomials

Chapter 18 Orthogonal Polynomials

35: 18.22 Hahn Class: Recurrence Relations and Differences

§18.22(i) Recurrence Relations in n

§18.22(ii) Difference Equations in x

§18.22(iii) x -Differences

36: Bibliography D

37: Bibliography L

38: Bibliography S

39: Bibliography G

40: Bibliography H

§18.22(i) Recurrence Relations in $n$

§18.22(ii) Difference Equations in $x$

§18.22(iii) $x$ -Differences