Theta functions and transformations of bilateral basic hypergeometric series
Number Theory
2026-05-15 v2 Classical Analysis and ODEs
Combinatorics
Abstract
We establish new transformation formulas involving theta functions and certain bilateral basic hypergeometric series. From these formulas, we construct companion -series for a class of -series such that the asymptotic expansion of their quotient admits a simple closed form. This allows us to prove several conjectures of McIntosh on asymptotic transformations of -series. Moreover, our results extend some identities of Ramanujan and McIntosh.
Cite
@article{arxiv.2605.05094,
title = {Theta functions and transformations of bilateral basic hypergeometric series},
author = {Nian Hong Zhou},
journal= {arXiv preprint arXiv:2605.05094},
year = {2026}
}