Orthogonal polynomials with the Prudnikov-type weights

Abstract

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