arXiv math/03022512003-02-20math.CAmath.RT

Continuous Hahn functions as Clebsch-Gordan coefficients

Wolter Groenevelt, Erik Koelink, Hjalmar Rosengren

发表信息：: Theory and applications of special functions, 221--284, Dev. Math., 13, Springer, New York, 2005

英文摘要：

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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