A New Product Formula for $$(z;q)_\infty $$, with Applications to Asymptotics
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.
Authors
- Hjalmar Rosengren (ORCID: https://orcid.org/0000-0001-6817-9279)
- Arash Arabi Ardehali
Institutions
- Sharif University of Technology (IR)
- Chalmers University of Technology (SE)
- University of Gothenburg (SE)
Publication Details
- Journal
- Constructive Approximation
- Published
- 2026-09-19
- DOI
- https://doi.org/10.1007/s00365-026-09783-2
- Primary Topic
- Advanced Mathematical Identities
- Type
- article
- Field-Weighted Citation Impact
- 0.00