New transformations for elliptic hypergeometric series on the root system An

Mathematics – Classical Analysis and ODEs

Scientific paper

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10 pages

Scientific paper

Recently, Kajihara gave a Bailey-type transformation relating basic hypergeometric series on the root system An, with different dimensions n. We give, with a new, elementary, proof, an elliptic analogue of this transformation. We also obtain further Bailey-type transformations as consequences of our result, some of which are new also in the case of basic and classical hypergeometric series.

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