Linearization and Krein-like functionals of hypergeometric orthogonal polynomials

Abstract

The Krein-like r-functionals of the hypergeometric orthogonal polynomials {pn(x)} with kernel of the form xs[ω(x)]βpm1 (x) . . . pmr(x), being ω(x) the weight function on the interval ∆ ∈ R, are determined by means of the Srivastava linearization method. The particular 2-functionals, which are particularly relevant in quantum physics, are explicitly given in terms of the degrees and the characteristic parameters of the polynomials. They include the well-known power moments and the novel Krein-like moments. Moreover, various related types of exponential and logarithmic functionals are also investigated.