Abstract
Summary: Spectral analysis of a certain doubly inifinite Jacobi operator leads to orthogonality relations for confluent hypergeometric functios, which are called Laguerre functions. This doubly infinite Jacobi operator corresponds to the action of a parabolic element of the Lie algebra su$(1,1).$ The Clebsch-Gordan coefficients for the tensor product representation of a positive and a negative discrete series representation of su$(1,1)$ are determined for the parabolic bases. They turn out to be multiples of Jacobi functions. From the interpretation of Laguerre polynomials and functions as overlap coefficients, we obtain a product formula for the Laguerre polynomials, given by an integral over Laguerre functions, Jacobi functions and continuous dual Hahn polynomials.
[ Ryszard Szwarc (Wroclaw) ]
Original language | Undefined/Unknown |
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Pages (from-to) | 329-352 |
Number of pages | 24 |
Journal | Indagationes Mathematicae |
Volume | 14 |
Issue number | 3-4 |
DOIs | |
Publication status | Published - 2003 |
Bibliographical note
NEO/beschikbaarheidsdatum 2004/zie url/sbKeywords
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