ON ROGERS-RAMANUJAN-SLATER TYPE THETA FUNCTION IDENTITY

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 72

Volume : 10 , Issue : 2
DOI: https://doi.org/10.56827/JRSMMS.2023.1002.2
Author :
Jian Cao (School of Mathematics, Hangzhou Normal University, Hangzhou City 311121, Zhejiang Province, People s Republic of CHINA)
Sama Arjika (Department of Mathematics and Informatics, University of Agadez, Post Office Box: 199, Agadez, NIGER)
M. P. Chaudhary (International Scientific Research and Welfare Organization (Albert Einstein Chair Professor of Mathematical Sciences) New Delhi 110018, INDIA)

Abstract

The main purpose of this article is to prove two Rogers–Ramanujan–Slater type theta function identities related to $\varphi(q)$ and $\phi_{0}(q)$, which were earlier investigated by two legendary mathematicians of their time. The results presented in this paper are motivated essentially by recent works of Cao {\it et al.} (see [5]).

Keywords and Phrases

Theta function, Rogers-Ramanujan-Slater identity, Jacobi's triple-product identity.

A.M.S. subject classification

Primary 05A30, 11B65, 33D15, 33D45; Secondary 33D60, 39A13, 39B32.

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