Continuous biorthogonality of an elliptic hypergeometric function

Spiridonov, V.

doi:10.1090/S1061-0022-09-01073-5

Continuous biorthogonality of an elliptic hypergeometric function
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by V. P. Spiridonov
Translated by: the author

St. Petersburg Math. J. 20 (2009), 791-812

DOI: https://doi.org/10.1090/S1061-0022-09-01073-5

Published electronically: July 21, 2009

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Abstract:

A family of continuous biorthogonal functions related to an elliptic analog of the Gauss hypergeometric function is constructed. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. The relationship with the Sklyanin algebra and elliptic analogs of the Faddeev modular double are discussed in detail.

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