An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli

Abstract

A (k -1)-fold Eulerian series expansion is given for 11(1-qn)l, where the product runs over all positive integers n that Rre not congruent to 0i or -i modulo 2k + 1. The Rogers-Rarnanujan identities are the cases k =i 2andk 'i+1 =2.

Rogers-Schur-Ramanujan Type Identities for the M ( p , p ′) Minimal Models of Conformal Field Theory

“…The first major advance was made in the 70's when Andrews realized [20] that there were generalizations of (1.1) in terms of multiple sums of the form…”

On transformation formulae of ordinary hypergeometric series

“…The celebrated Bailey [2] transform was extensively used to obtain transformation formulae of ordinary hypergeometric series and basic hypergeometric series with help of known summation formulae. The technique provided by Bailey [2] and Slater [3], [4] motivated a number of mathematicians namely Andrews [7], [8], Verma and Jain [9], [10], U.B.Singh [12], Agarwal [13], S.P. Singh [14], Denis et.al.…”

Parity in partition identities

“…Then for all n 0, A k,a (n) = B k,a (n). After Gordon's proof of this theorem in 1961 [16], there was subsequently discovered a generating function version in 1974 [6]: for |q| < 1 where N j = n j + n j+1 + · · · + n k−1 , and (A; q) n = (A) n = (1 − A)(1 − Aq) · · · (1 − Aq n−1 ).…”