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math.CA2024
Elliptic hypergeometric functions: integrals versus series
Vyacheslav P. Spiridonov
The univariate elliptic beta integral is represented as a bilinear combination of infinite very-well-poised elliptic hypergeometric series representing the sum of residu…
math.CA2023
Infinite elliptic hypergeometric series: convergence and difference equations
D. I. Krotkov, V. P. Spiridonov
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 d…