Orthogonal polynomials for the weight $x^{\nu }\exp (-x-t/x)$

Abstract

Orthogonal polynomials for the weight $x^{\nu }\exp (-x-t/x),x,t>0,\nu \in \mathbb{R}$ are investigated. Differential-difference equations, recurrence relations, explicit representations, generating functions and Rodrigues-type formula are obtained.