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Infinite Elliptic Hypergeometric Series: Convergence and Difference Equations by Krotkov, D. I.; Spiridonov, V. P. is a scholarly article available to read on EtoBox.

What is Infinite Elliptic Hypergeometric Series: Convergence and Difference Equations about?

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, we describe some constraints on the parameters when they do converge. In particular, we lift the Hardy-Littlewood criterion on the convergence of $q$-hypergeometric series for $|q|=1, \, q^n\neq 1$, to the elliptic level and prove convergence of the infinite ${}_{r+1}V_r$ very-well poised elliptic hypergeometric series for restricted values of $q$.

Author

Krotkov, D. I.; Spiridonov, V. P.

Published

2023

Language

EN