Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions

Abstract

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan's forty identities for Rogers-Ramanujan functions. Furthermore, we give partition theoretic interpretations of some of our modular relations.

Special Issue: “q-Series and Related Topics in Special Functions and Analytic Number Theory”—Foreword

“…Quite frequently, these special issues are devoted exclusively to specific topics and/or are dedicated respectfully to commemorate the celebrated works of renowned research scientists. The following Special Issue: "q-Series and Related Topics in Special Functions and Analytic Number Theory" (see [1][2][3][4][5][6][7][8] below) is an outcome of the ongoing importance and popularity of such topics as Basic (or q-) Series and Basic (or q-) Polynomials.…”