A New Product Formula for $$(z;q)_\infty $$, with Applications to Asymptotics

Constructive Approximation 2026 Open access

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Authors: Arash Arabi Ardehali, Hjalmar Rosengren
DOI: 10.1007/s00365-026-09783-2
Cited by: 0

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.

Fields of Study & Subjects

Advanced Mathematical Identities Mathematical functions and polynomials Mathematical Inequalities and Applications

Publication details

Journal / source
Constructive Approximation
Publication date
19 September 2026
Language
EN