Mathematics > Number Theory
[Submitted on 3 May 2018 (v1), last revised 26 Jan 2019 (this version, v2)]
Title:On a theta product of Jacobi and its applications to $q$-gamma products
View PDFAbstract:We give a new proof for a product formula of Jacobi which turns out to be equivalent to a $q$-trigonometric product which was stated without proof by Gosper. We apply this formula to derive a $q$-analogue for the Gauss multiplication formula for the gamma function. Furthermore, we give explicit formulas for short products of $q$-gamma functions.
Submission history
From: Mohamed El Bachraoui [view email][v1] Thu, 3 May 2018 05:25:51 UTC (10 KB)
[v2] Sat, 26 Jan 2019 06:27:35 UTC (11 KB)
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