On the theory of orthogonal polynomials for the weight x^ν exp (−x − t/x). I

Abstract

Orthogonal polynomials for the weight $x^{\nu }\exp (-x-t/x),x,t>0,\nu \in \mathbb{R}$ are investigated without the use of the Chen–Ismail ladder operators approach. Differential and differential–difference equations are deduced.

Keywords:

• Classical orthogonal polynomials
• Laguerre polynomials
• modified Bessel function
• generalized hypergeometric function

AMS Subject Classifications:

• 33C10
• 42C05
• 44A15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was partially supported by CMUP, which is financed by national funds through Fundação para a Ciência e a Tecnologia (FCT) (Portugal), under the project with reference UIDB/00144/2020.