Several q-series related to Ramanujan’s theta functions

Quite recently, the first author investigated vanishing coefficients of the arithmetic progressions in several q -series expansions. In this paper, we further study the signs of coefficients in two q -series expansions and establish some interlinked identities for several q -series expansions by mea...

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Published in:The Ramanujan journal 2020-12, Vol.53 (3), p.705-724
Main Authors: Tang, Dazhao, Xia, Ernest. X. W.
Format: Article
Language:English
Subjects:
Combinatorial analysis
Combinatorics
Dissection
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Progressions
Series (mathematics)
Series expansion
Thermal expansion
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description Quite recently, the first author investigated vanishing coefficients of the arithmetic progressions in several q -series expansions. In this paper, we further study the signs of coefficients in two q -series expansions and establish some interlinked identities for several q -series expansions by means of Ramanujan’s theta functions. We obtain the 5-dissections of these two q -series and give combinatorial interpretations for these dissections. Moreover, we obtain four q -series identities involving the aforementioned q -series, two of which were proved by Kim and Toh via modular forms.
doi_str_mv 10.1007/s11139-019-00187-4
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subjects Combinatorial analysis
Combinatorics
Dissection
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Progressions
Series (mathematics)
Series expansion
Thermal expansion
title Several q-series related to Ramanujan’s theta functions
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