An extended scheme of classical special functions
Classical Analysis and ODEs
2024-03-26 v1
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 -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.
Cite
@article{arxiv.2403.16264,
title = {An extended scheme of classical special functions},
author = {Vyacheslav P. Spiridonov},
journal= {arXiv preprint arXiv:2403.16264},
year = {2024}
}
Comments
16 pp., written for a book dedicated to R. Askey and his influence on the theory of special functions