A q-summation formula, the continuous q-Hahn polynomials and the big q-Jacobi polynomials

Zhi Guo Liu

doi:10.1016/j.jmaa.2014.05.047

A q-summation formula, the continuous q-Hahn polynomials and the big q-Jacobi polynomials

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

5 Scopus citations

Abstract

Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah-Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah-Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities.

Original language	English
Pages (from-to)	1045-1064
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	419
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.05.047
State	Published - 15 Nov 2014

Keywords

Nassrallah-Rahman integral
Q-Hahn polynomials
Q-Jacobi polynomials
Q-series
Q-summation

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10.1016/j.jmaa.2014.05.047

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abstract = "Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah-Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah-Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities.",

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T1 - A q-summation formula, the continuous q-Hahn polynomials and the big q-Jacobi polynomials

AU - Liu, Zhi Guo

PY - 2014/11/15

Y1 - 2014/11/15

N2 - Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah-Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah-Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities.

AB - Using a general q-summation formula, we derive a generating function for the q-Hahn polynomials, which is used to give a complete proof of the orthogonality relation for the continuous q-Hahn polynomials. A new proof of the orthogonality relation for the big q-Jacobi polynomials is also given. A simple evaluation of the Nassrallah-Rahman integral is derived by using this summation formula. A new q-beta integral formula is established, which includes the Nassrallah-Rahman integral as a special case. The q-summation formula also allows us to recover several strange q-series identities.

KW - Nassrallah-Rahman integral

KW - Q-Hahn polynomials

KW - Q-Jacobi polynomials

KW - Q-series

KW - Q-summation

UR - https://www.scopus.com/pages/publications/84903436273

U2 - 10.1016/j.jmaa.2014.05.047

DO - 10.1016/j.jmaa.2014.05.047

M3 - 文章

AN - SCOPUS:84903436273

SN - 0022-247X

VL - 419

SP - 1045

EP - 1064

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

A q-summation formula, the continuous q-Hahn polynomials and the big q-Jacobi polynomials

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Keywords

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