𝑞-Bessel functions and Rogers-Ramanujan type identities

Ismail, Mourad; Zhang, Ruiming

doi:10.1090/proc/13078

$q$-Bessel functions and Rogers-Ramanujan type identities
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by Mourad E. H. Ismail and Ruiming Zhang PDF

Proc. Amer. Math. Soc. 146 (2018), 3633-3646 Request permission

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.

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