New Bessel Identities from Laguerre Polynomials

Abstract

For large order, Laguerre polynomials can be approximated by Bessel functions near the origin. This can be used to turn many Laguerre identities into corresponding identities for Bessel functions. We will illustrate this idea with a number of examples. In particular, we will derive a generalization of a identity due to Sonine, which appears to be new.