A New Product Formula for (z;q)∞, with Applications to Asymptotics
Journal article, 2026
We express the q-Pochhammer symbol (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.
q-Pochhammer symbol
Asymptotic expansion
Quantum dilogarithm
q-gamma function
Author
Arash Arabi Ardehali
Sharif University of Technology
Hjalmar Rosengren
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Constructive Approximation
0176-4276 (ISSN) 1432-0940 (eISSN)
Vol. In PressSubject Categories (SSIF 2025)
Mathematical Analysis
DOI
10.1007/s00365-026-09783-2