Reciprocity theorems involving the q-gamma function

Mohamed El Bachraoui; James Griffin

doi:10.1007/s11139-016-9872-3

Reciprocity theorems involving the q-gamma function

Mohamed El Bachraoui, James Griffin

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

In one of his notebooks, Ramanujan stated but did not prove an identity for a ratio of gamma functions involving two separate variables. Such an identity was referred to as a reciprocity theorem due to the symmetry relations between the variables. The two variable result was later proved and generalized to several variables by Berndt and Koukoulopoulos (Proc Am Math Soc 601:2369–2373, 2007). In this paper, we state and prove similar reciprocity theorems for ratios of q-gamma functions involving two and more variables.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Ramanujan Journal
DOIs	https://doi.org/10.1007/s11139-016-9872-3
Publication status	Accepted/In press - Jan 31 2017

Keywords

q-Analogs
q-Gamma function
Reciprocity theorem

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s11139-016-9872-3

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AB - In one of his notebooks, Ramanujan stated but did not prove an identity for a ratio of gamma functions involving two separate variables. Such an identity was referred to as a reciprocity theorem due to the symmetry relations between the variables. The two variable result was later proved and generalized to several variables by Berndt and Koukoulopoulos (Proc Am Math Soc 601:2369–2373, 2007). In this paper, we state and prove similar reciprocity theorems for ratios of q-gamma functions involving two and more variables.

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KW - Reciprocity theorem

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ER -

Reciprocity theorems involving the q-gamma function

Abstract

Keywords

ASJC Scopus subject areas

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