q-integral and moment representations for q-orthogonal polynomials

Mourad E.H. Ismail; Dennis Stanton

doi:10.4153/CJM-2002-027-2

q-integral and moment representations for q-orthogonal polynomials

Mourad E.H. Ismail, Dennis Stanton

School of Mathematics

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26 Scopus citations

Abstract

We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function ε_q.

Original language	English (US)
Pages (from-to)	709-735
Number of pages	27
Journal	Canadian Journal of Mathematics
Volume	54
Issue number	4
DOIs	https://doi.org/10.4153/CJM-2002-027-2
State	Published - Aug 2002

Keywords

Al-Salam-Chihara polynomials
Associated polynomials
Continuous q-ultraspherical polynomials
Generating functions
q-difference equations
q-integral
q-orthogonal polynomials

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10.4153/CJM-2002-027-2

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abstract = "We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.",

keywords = "Al-Salam-Chihara polynomials, Associated polynomials, Continuous q-ultraspherical polynomials, Generating functions, q-difference equations, q-integral, q-orthogonal polynomials",

author = "Ismail, \{Mourad E.H.\} and Dennis Stanton",

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T1 - q-integral and moment representations for q-orthogonal polynomials

AU - Ismail, Mourad E.H.

AU - Stanton, Dennis

PY - 2002/8

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N2 - We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.

AB - We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.

KW - Al-Salam-Chihara polynomials

KW - Associated polynomials

KW - Continuous q-ultraspherical polynomials

KW - Generating functions

KW - q-difference equations

KW - q-integral

KW - q-orthogonal polynomials

UR - https://www.scopus.com/pages/publications/0036686027

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DO - 10.4153/CJM-2002-027-2

M3 - Article

AN - SCOPUS:0036686027

SN - 0008-414X

VL - 54

SP - 709

EP - 735

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 4

ER -

q-integral and moment representations for q-orthogonal polynomials

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