Expansion of analytic functions in q-orthogonal polynomials

Moritz Simon; Sergei Suslov

doi:10.1007/s11139-007-9110-0

Expansion of analytic functions in q-orthogonal polynomials

Moritz Simon, Sergei Suslov

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey-Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.

Original language	English (US)
Pages (from-to)	281-303
Number of pages	23
Journal	Ramanujan Journal
Volume	19
Issue number	3
DOIs	https://doi.org/10.1007/s11139-007-9110-0
State	Published - 2009

Keywords

Al-Salam and Chihara polynomials
Askey-Wilson polynomials
Basic hypergeometric functions
Chebyshev polynomials
Continuous big q-Hermite polynomials
Continuous dual q-Hahn polynomials
Continuous q-Hermite polynomials
Continuous q-Jacobi polynomials
Continuous q-ultraspherical polynomials
Jacobi polynomials
q-orthogonal polynomials

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s11139-007-9110-0

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title = "Expansion of analytic functions in q-orthogonal polynomials",

abstract = "A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey-Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.",

keywords = "Al-Salam and Chihara polynomials, Askey-Wilson polynomials, Basic hypergeometric functions, Chebyshev polynomials, Continuous big q-Hermite polynomials, Continuous dual q-Hahn polynomials, Continuous q-Hermite polynomials, Continuous q-Jacobi polynomials, Continuous q-ultraspherical polynomials, Jacobi polynomials, q-orthogonal polynomials",

author = "Moritz Simon and Sergei Suslov",

year = "2009",

doi = "10.1007/s11139-007-9110-0",

language = "English (US)",

volume = "19",

pages = "281--303",

journal = "Ramanujan Journal",

issn = "1382-4090",

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T1 - Expansion of analytic functions in q-orthogonal polynomials

AU - Simon, Moritz

AU - Suslov, Sergei

PY - 2009

Y1 - 2009

N2 - A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey-Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.

AB - A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey-Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.

KW - Al-Salam and Chihara polynomials

KW - Askey-Wilson polynomials

KW - Basic hypergeometric functions

KW - Chebyshev polynomials

KW - Continuous big q-Hermite polynomials

KW - Continuous dual q-Hahn polynomials

KW - Continuous q-Hermite polynomials

KW - Continuous q-Jacobi polynomials

KW - Continuous q-ultraspherical polynomials

KW - Jacobi polynomials

KW - q-orthogonal polynomials

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DO - 10.1007/s11139-007-9110-0

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AN - SCOPUS:70350357328

SN - 1382-4090

VL - 19

SP - 281

EP - 303

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

ER -

Expansion of analytic functions in q-orthogonal polynomials

Abstract

Keywords

ASJC Scopus subject areas

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