$q$-Bessel Functions and Rogers-Ramanujan Type Identities

Abstract

We evaluate $q$-Bessel functions at an infinite sequence of points and introduce a generalization of the Ramanujan function and give an extension of the $m$-version of the Rogers-Ramanujan identities. We also prove several generating functions for Stieltjes-Wigert polynomials with argument depending on the degree. In addition we give several Rogers-Ramanujan type identities.