Multiplication Formulas for the Elliptic Gamma Function
G. Felder, A. Varchenko
TL;DR
This paper establishes multiplication formulas for the elliptic gamma function, extending classical formulas for the Euler and trigonometric gamma functions to a more general elliptic setting.
Contribution
It introduces new multiplication formulas for the elliptic gamma function, generalizing known formulas for Euler and trigonometric gamma functions.
Findings
Proves multiplication formulas for the elliptic gamma function.
Degenerations recover classical multiplication formulas.
Extends gamma function identities to elliptic functions.
Abstract
The elliptic gamma function is a generalization of the Euler gamma function. Its trigonometric and rational degenerations are the Jackson q-gamma function and the Euler gamma function. We prove multiplication formulas for the elliptic gamma function, whose degenerations are the Gauss-Askey multiplication formula for the Euler and trigonometric gamma functions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Mathematical functions and polynomials