Multiple elliptic hypergeometric series. An approach from the Cauchy determinant

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A multiple generalization of elliptic hypergeometric series is investigated and a duality transformation for multiple hypergeometric series is proposed. Our duality transformation obtained from an identity arising from the Cauchy determinant formula for Weierstrass sigma functions, by spcialization of a particular form.

A few typos were corrected. We added our multiple Bailey transformation formulas in the trigonometric (basic) case. to appear in Indag. Math

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