On a theta product of Jacobi and its applications to q-gamma products

2018/05/03 by Bachraoui, Mohamed El, Sándor, József
#33B15 #33E05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1805.01121

Abstract

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.

Related

• Some new sums of q-trigonometric and related functions through a theta product of Jacobi
• Theory of general theta relations, addition formulas, and theta constants identities
• Special values of q-gamma products
• Multiplication Formulas for the Elliptic Gamma Function
• Two generalizations of Jacobi's derivative formula