Two-dimensional contiguous relations for linearization coefficients of orthogonal polynomials in the Askey-scheme

2022/06/10 by Howard S. Cohl, Cohl, Howard S., Lisa Ritter +1
Mathematics · #33C45 #33C65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2206.05230

openalex publication_date 2022/06/10 · openalex created_date 2022/06/14 · openalex updated_date 2026/07/28

Abstract

We produce two-dimensional contiguous relations for generalized hypergeometric functions by starting with linearization coefficients for some continuous generalized hypergeometric orthogonal polynomials in the Askey-scheme.

Related

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme
• A unified construction of all the hypergeometric and basic\n hypergeometric families of orthogonal polynomial sequences
• Discrete orthogonality of hypergeometric polynomial sequences on linear and quadratic lattices
• Topics in special functions