On modular relations for the functions analogous to Roger’s-Ramanujan functions with applications to partitions

Adiga, Chandrashekara S and Vasuki, K R and Srivatsa Kumar, B R (2014) On modular relations for the functions analogous to Roger’s-Ramanujan functions with applications to partitions. South East Asian Journal of Mathematics and Mathematical Science, 6 (2). pp. 131-144. ISSN 0972-7752

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Abstract

In this paper we establish modular relations involving the functions, S(q)=∑_(n=0)^∞▒q^(n^2+n)/〖(q^2; q^2)〗_∞ and T(q)=∑_(n=0)^∞▒q^(n^2 )/〖(q^2; q^2)〗_∞ , which are analogous to Ramanujan’s modular identities. Furthermore, we extract some partition results from them

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