Geodesic
Infinite elliptic hypergeometric series: convergence and difference equations
Sbornik. Mathematics, Tome 214 (2023) no. 12, pp. 1751-1778

Voir la notice de l'article provenant de la source Math-Net.Ru

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 ${|q|=1}$, $q^n\neq 1$, to the elliptic level and prove the convergence of infinite very-well poised elliptic hypergeometric ${}_{r+1}V_r$-series for restricted values of $q$. Bibliography: 13 titles.
Keywords: elliptic hypergeometric series, finite difference equations, Padé approximation. 
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     author = {D. I. Krotkov and V. P. Spiridonov},
     title = {Infinite elliptic hypergeometric series: convergence and difference equations},
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     pages = {1751--1778},
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D. I. Krotkov; V. P. Spiridonov. Infinite elliptic hypergeometric series: convergence and difference equations. Sbornik. Mathematics, Tome 214 (2023) no. 12, pp. 1751-1778. http://geodesic.mathdoc.fr/item/SM_2023_214_12_a4/