Quadratic q-exponentials and connection coefficient problems

Mourad E.H. Ismail; Mizan Rahman; Dennis Stanton

doi:10.1090/s0002-9939-99-05017-0

Quadratic q-exponentials and connection coefficient problems

Mourad E.H. Ismail, Mizan Rahman, Dennis Stanton

School of Mathematics

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

15 Scopus citations

Abstract

We establish expansion formulas of q-exponential functions in terms of continuous g-ultraspherical polynomials, continuous q-Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.

Original language	English (US)
Pages (from-to)	2931-2941
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	127
Issue number	10
DOIs	https://doi.org/10.1090/s0002-9939-99-05017-0
State	Published - 1999

Keywords

Askey-wilson polynomials
Continuous q-ultraspherical polynomials
Q-bessel functions
Q-exponential functions

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10.1090/s0002-9939-99-05017-0

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title = "Quadratic q-exponentials and connection coefficient problems",

abstract = "We establish expansion formulas of q-exponential functions in terms of continuous g-ultraspherical polynomials, continuous q-Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.",

keywords = "Askey-wilson polynomials, Continuous q-ultraspherical polynomials, Q-bessel functions, Q-exponential functions",

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

year = "1999",

doi = "10.1090/s0002-9939-99-05017-0",

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TY - JOUR

T1 - Quadratic q-exponentials and connection coefficient problems

AU - Ismail, Mourad E.H.

AU - Rahman, Mizan

AU - Stanton, Dennis

PY - 1999

Y1 - 1999

N2 - We establish expansion formulas of q-exponential functions in terms of continuous g-ultraspherical polynomials, continuous q-Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.

AB - We establish expansion formulas of q-exponential functions in terms of continuous g-ultraspherical polynomials, continuous q-Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.

KW - Askey-wilson polynomials

KW - Continuous q-ultraspherical polynomials

KW - Q-bessel functions

KW - Q-exponential functions

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U2 - 10.1090/s0002-9939-99-05017-0

DO - 10.1090/s0002-9939-99-05017-0

M3 - Article

AN - SCOPUS:22844455171

SN - 0002-9939

VL - 127

SP - 2931

EP - 2941

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 10

ER -

Quadratic q-exponentials and connection coefficient problems

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