Enviar artigo por via de e-mail Infinite elliptic hypergeometric series: convergence and diffrence equations
- Autores: Krotkov D.I.1, Spiridonov V.P.2,1
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Afiliações:
- HSE University
- Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
- Edição: Volume 214, Nº 12 (2023)
- Páginas: 106-134
- Seção: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/147930
- DOI: https://doi.org/10.4213/sm9874
- ID: 147930
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Resumo
We derive finite difference equations of infinite order for theta-hypergeometric series and investigate the space of their solutions. In general, such infinite series diverge, and we describe some constraints on the parameters when they do converge. In particular, we lift the Hardy-Littlewood criterion of the convergence of q-hypergeometric series for |q|=1, qn≠1, to the elliptic level and prove the convergence of infinite very-well poised elliptic hypergeometric r+1Vr-series for restricted values of q.
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Sobre autores
Danil Krotkov
HSE University
Email: math-net2025_06@mi-ras.ru
Vyacheslav Spiridonov
Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics; HSE University
Autor responsável pela correspondência
Email: math-net2025_06@mi-ras.ru
Doctor of physico-mathematical sciences, no status
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