Continuous Hahn functions as Clebsch-Gordan coefficients

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An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomial $_3F_2$-hypergeometric functions that we consider as continuous Hahn functions. An integral transform pair with continuous Hahn functions as kernels is also proved. These results have an interpretation for the tensor product decomposition of a positive and a negative discrete series representation of $\su(1,1)$ with respect to hyperbolic bases, where the Clebsch-Gordan coefficients are continuous Hahn functions.

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Classical Analysis and ODEs, Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/120473

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0302251
 http://arxiv.org/abs/math/0302251
 Theory and applications of special functions, 221--284, Dev. Math., 13, Springer, New York, 2005

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arXiv