A New Product Formula for $$(z;q)_\infty $$, with Applications to Asymptotics
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Abstract
Abstract We express the q -Pochhammer symbol $$(z;q)_\infty $$ ( z ; q ) ∞ as an infinite product of gamma functions, analogously to how Narukawa expressed the elliptic gamma function as an infinite product of hyperbolic gamma functions. This identity is used to obtain asymptotic expansions when q tends to 1.
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Authors: Arash Arabi Ardehali, Hjalmar Rosengren
Institutions: University of Gothenburg, Chalmers University of Technology, Sharif University of Technology