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A Family of Integral Transformations and Basic Hypergeometric Series

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Abstract

We present a conjecture giving a family of commuting operators {I(α)|α ∈ C}, in terms of n-fold integral transformations. For the simplest case n=2, the commutativity is proved by using several summation and transformation formulas for the basic hypergeometric series.

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Authors and Affiliations

  1. Graduate School of Mathematical Science, University of Tokyo, Tokyo, Japan

    Jun'ichi Shiraishi

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  1. Jun'ichi Shiraishi
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Communicated by L. Takhtajan

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Shiraishi, J. A Family of Integral Transformations and Basic Hypergeometric Series. Commun. Math. Phys. 263, 439–460 (2006). https://doi.org/10.1007/s00220-005-1504-5

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  • DOI: https://doi.org/10.1007/s00220-005-1504-5

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