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Transformation and Reduction Formulas for Two‐Variable Hypergeometric Functions on the Sphere S2

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We classify the two‐variable hypergeometric functions that arise as eigenfunctions of the Laplace‐Beltrami operator on S 2 and characterize these functions in terms of elements in the enveloping algebra of so(3). This operator characterization is used to derive transformation and reduction formulas for the functions.
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Document Type: Research Article

Publication date: October 1, 1980

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