Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral

Zhi Guo Liu

doi:10.1016/j.jmaa.2016.06.005

Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral

Zhi Guo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

8 Scopus citations

Abstract

Ramanujan's reciprocity theorem may be considered as a three-variable extension of Jacobi's triple product identity. Using the method of q-partial differential equations, we extend Ramanujan's reciprocity theorem to a seven-variable reciprocity formula. Using the same method, the Andrews-Askey integral formula is extended to a q-integral formula which has seven parameters with base q.

Original language	English
Pages (from-to)	1110-1129
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	443
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2016.06.005
State	Published - 15 Nov 2016

Keywords

Al-Salam-Verma integral
Analytic functions
Andrews-Askey integral
Q-integrals
Q-partial differential equations
Ramanujan's reciprocity theorem

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abstract = "Ramanujan's reciprocity theorem may be considered as a three-variable extension of Jacobi's triple product identity. Using the method of q-partial differential equations, we extend Ramanujan's reciprocity theorem to a seven-variable reciprocity formula. Using the same method, the Andrews-Askey integral formula is extended to a q-integral formula which has seven parameters with base q.",

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AB - Ramanujan's reciprocity theorem may be considered as a three-variable extension of Jacobi's triple product identity. Using the method of q-partial differential equations, we extend Ramanujan's reciprocity theorem to a seven-variable reciprocity formula. Using the same method, the Andrews-Askey integral formula is extended to a q-integral formula which has seven parameters with base q.

KW - Al-Salam-Verma integral

KW - Analytic functions

KW - Andrews-Askey integral

KW - Q-integrals

KW - Q-partial differential equations

KW - Ramanujan's reciprocity theorem

UR - https://www.scopus.com/pages/publications/84973539316

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DO - 10.1016/j.jmaa.2016.06.005

M3 - 文章

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JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral

Abstract

Keywords

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