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

TL;DR

This paper develops two-dimensional contiguous relations for hypergeometric functions by leveraging linearization coefficients of orthogonal polynomials within the Askey-scheme, advancing the understanding of their interrelations.

Contribution

It introduces new two-dimensional contiguous relations for hypergeometric functions derived from linearization coefficients of Askey-scheme orthogonal polynomials.

Findings

Derived explicit two-dimensional contiguous relations.

Connected hypergeometric functions with orthogonal polynomial linearization coefficients.

Enhanced tools for analyzing hypergeometric functions in mathematical physics.

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.