Year: 2024
Type: preprint
Abstract: A unifying scheme of classical special functions of hypergeometric type obeying orthogonality or biorthogonality relations is described. It expands the Askey scheme of classical orthogonal polynomials and its $q$-analogue based on the Askey--Wilson polynomials. On the top, it has two-index biorthogonal functions formed from elliptic hypergeometric series with the absolutely continuous measure determined by the elliptic beta integral. A new result is an inclusion of complex hypergeometric functions into the scheme. Its further potential generalizations are discussed as well.
Source: arXiv (Cornell University)
Author: Spiridonov, Vyacheslav P.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393213121