Applications of q-Taylor theorems

Mourad E.H. Ismail; Dennis Stanton

doi:10.1016/S0377-0427(02)00644-1

Applications of q-Taylor theorems

Mourad E.H. Ismail, Dennis Stanton

Mathematics

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

34 Scopus citations

Abstract

We establish two new q-analogues of a Taylor series expansion for polynomials using special Askey-Wilson polynomial bases. Combining these expansions with an earlier expansion theorem we derive inverse relations and evaluate certain linearization coefficients. Byproducts include new summation theorems, new results on a q-exponential function, and quadratic transformations for q-series.

Original language	English (US)
Pages (from-to)	259-272
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	153
Issue number	1-2
DOIs	https://doi.org/10.1016/S0377-0427(02)00644-1
State	Published - Apr 1 2003

Bibliographical note

Funding Information:
Part of this work was done while the authors were visiting the Liu Bie Ju Center of Mathematical Sciences of City University of Hong Kong and they gratefully acknowledge the financial support and the hospitality of the City University of Hong Kong.

Keywords

Askey-Wilson operators
Connection relations
Polynomial bases
Summation theorems
q-exponential function

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AB - We establish two new q-analogues of a Taylor series expansion for polynomials using special Askey-Wilson polynomial bases. Combining these expansions with an earlier expansion theorem we derive inverse relations and evaluate certain linearization coefficients. Byproducts include new summation theorems, new results on a q-exponential function, and quadratic transformations for q-series.

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KW - Connection relations

KW - Polynomial bases

KW - Summation theorems

KW - q-exponential function

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Applications of q-Taylor theorems

Abstract

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Keywords

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