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 |
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Pages (from-to) | 1-12 |
Number of pages | 12 |
Journal | Ramanujan Journal |
DOIs | |
Publication status | Accepted/In press - Jan 31 2017 |
Keywords
- q-Analogs
- q-Gamma function
- Reciprocity theorem
ASJC Scopus subject areas
- Algebra and Number Theory