Ultraspherical type generating functions for orthogonal polynomials

Abstract

We characterize, up to a conjecture, probability distributions of all order finite moments having ultraspherical type generating functions for orthogonal polynomials.

Some proofs are shortened. There is an insight into the stated conjecture

References in corpus (2)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• On a class of free Levy laws related to a regression problem

Cited by in corpus (5)

• On generalized Cauchy-Stieltjes transforms of some Beta distributions
• Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples
• Generating functions of Cauchy-Stieltjes type for orthogonal polynomials
• Topics on Meixner families
• A characterization of ultraspherical, Hermite, and Chebyshev polynomials of the first kind