Associated Laguerre and Hermite polynomials

Abstract

Synopsis Explicit orthogonality relations are found for the associated Laguerre and Hermite polynomials. One consequence is the construction of the [ n − 1/ n ] Padé approximation to Ψ( a + 1, b ; x )/Ψ( a, b; x ), where Ψ( a, b; x ) is the second solution to the confluent hypergeometric differential equation that does not grow rapidly at infinity.