Some modular relations for the Göllnitz-Gordon functions by an even-odd method
type: Item
instance of: scholarly article
title: Some modular relations for the Göllnitz-Gordon functions by an even-odd method
zbMATH Open document ID: 1294.11183
author: Juan-Miguel Gracia
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-11-15T00:00:00Z
review text: The Göllnitz-Gordon functions are defined as \[ S(q):=\sum_{n=0}^{\infty}\frac{(-q;q^2)_n}{(q^2;q^2)_n}q^{n^2}, \] and \[ T(q):=\sum_{n=0}^{\infty}\frac{(-q;q^2)_n}{(q^2;q^2)_n}q^{n^2+2n}, \] where, as usual, we let \((a;q)_n:=\prod_{j=0}^{n-1}(1-aq^j)\). In this paper the authors provide new proofs of fifteen modular relations for the Göllnitz-Gordon functions, established by \textit{S.-S. Huang} [J. Number Theory 68, No. 2, 178--216 (1998; Zbl 0892.11016)] and \textit{S.-L. Chen} and \textit{S.-S. Huang} [J. Number Theory 93, No. 1, 58--75 (2002; Zbl 1059.11020)], and prove ten new modular relations for these functions using an even-odd method.
reviewed by: Ricardo Mamede
Mathematics Subject Classification ID: 11P84
Mathematics Subject Classification ID: 11B65
zbMATH DE Number: 5971761
zbMATH Keywords: modular relation
zbMATH Keywords: Rogers-Ramanujan function
zbMATH Keywords: Göllnitz-Gordon function
zbMATH Keywords: even-odd method
zbMATH Keywords: Ramanujan's general theta function
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.08.059
OpenAlex ID: W1982715416
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DOI: 10.1016/J.JMAA.2011.08.059
description: scientific article; zbMATH DE number 5971761