# Orthogonal polynomials with the Prudnikov-type weights

## TL;DR

This paper introduces new sequences of orthogonal polynomials associated with specific weight functions involving exponential and Bessel functions, providing their recurrence relations, explicit formulas, and generating functions.

## Contribution

It presents novel orthogonal polynomials related to Prudnikov-type weights, including their fundamental properties and explicit representations.

## Key findings

- Derived recurrence relations for the new polynomials
- Obtained explicit representations and generating functions
- Established Rodrigues-type formulae for the polynomials

## Abstract

New sequences of orthogonal polynomials with respect to the weight functions $e^{-x} \rho_\nu(x),\ e^{- 1/x} x^{-1} \rho_{\nu} (x), \rho_{\nu}(x)= 2 x^{\nu/2} K_\nu(2\sqrt x),\ x >0, \nu \in \mathbb{R}$, where $K_\nu(z)$ is the modified Bessel function, are investigated. The recurrence relations, explicit representations, generating functions and Rodrigues-type formulae are obtained.