An extended scheme of classical special functions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913281465122816 |
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| author | Spiridonov, Vyacheslav P. |
| author_facet | Spiridonov, Vyacheslav P. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_16264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An extended scheme of classical special functions Spiridonov, Vyacheslav P. Classical Analysis and ODEs 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. |
| title | An extended scheme of classical special functions |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.16264 |