ON ROGERS-RAMANUJAN-SLATER TYPE THETA FUNCTION IDENTITY

Jian  Cao; Sama  Arjika; M. P.  Chaudhary

doi:10.56827/JRSMMS.2023.1002.2

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

DOI: https://doi.org/10.56827/JRSMMS.2023.1002.2

Keywords: Theta function, Rogers-Ramanujan-Slater identity, Jacobi’s triple-product identity.

Abstract

The main purpose of this article is to prove two Rogers–Ramanujan–Slater type theta function identities related to φ(q) and ϕ0(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 et al. (see [5]).