On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity

Abstract

The authors establish a set of two new relationships involving q-product identities, Ralpha, Rbeta, and Rm (m = 1, 2, 3, . . .) functions; and answer a open question of Srivastava et al. [18]. The present work is motivated and based upon recent findings of Chaudhary et al. [8].

Keywords

• theta-function identities
• ra, rb, and rm functions
• jacobi's triple-product identity
• q-product identities
• rogers-ramanujan continued fraction
• rogers-ramanujan identities