A Multiparameter Summation Formula for Theta Functions
نویسنده
چکیده
We generalize Warnaar's elliptic extension of a Macdonald multi-parameter summation formula to Riemann surfaces of arbitrary genus. We start by a brief outline of the general theory of hypergeometric type series built from Jacobi theta functions [12, 13] (its extension to integrals [15] is not touched at all). Within this approach univariate elliptic hypergeometric series are defined as the series n c n for which h(n) = c n+1 /c n is an elliptic function of n considered as a continuous complex variable. Normalizing c 0 = 1, we see that all coefficients c n are obtained as products of h(k) for different k. Any elliptic function of order r + 1 can be represented as [18]:
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