Continuous Hahn functions as Clebsch-Gordan coefficients

Details Continuous Hahn functions as Clebsch-Gordan coefficients Continuous Hahn functions as Clebsch-Gordan coefficients

2003-02-20

arxiv.org/abs/math/0302251v1

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

Mathematics

Classical Analysis and ODEs

Scientific paper

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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