 Author
 Year
 2005
 Title
 A second addition formula for continuous qultraspherical polynomials
 Journal
 Developments in mathematics
 Volume
 13
 Pages (fromto)
 339360
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

This paper provides the details of Remark 5.4 in the author's paper "AskeyWilson polynomials as zonal spherical functions on the SU(2) quantum group", SIAM J. Math. Anal. 24 (1993), 795813. In formula (5.9) of the 1993 paper a twoparameter class of AskeyWilson polynomials was expanded as a finite Fourier series with a product of two 3phi2's as Fourier coefficients. The proof given there used the quantum group interpretation. Here this identity will be generalized to a 3parameter class of AskeyWilson polynomials being expanded in terms of continuous qultraspherical polynomials with a product of two 2phi2's as coefficients, and an analytic proof will be given for it. Then Gegenbauer's addition formula for ultraspherical polynomials and Rahman's addition formula for qBessel functions will be obtained as limit cases. This qanalogue of Gegenbauer's addition formula is quite different from the addition formula for continuous qultraspherical polynomials obtained by Rahman and Verma in 1986. Furthermore, the functions occurring as factors in the expansion coefficents will be interpreted as a special case of a system of biorthogonal rational functions with respect to the AskeyRoy qbeta measure. A degenerate case of this biorthogonality are Pastro's biorthogonal polynomials associated with the StieltjesWigert polynomials.
 Link
 Link
 Language
 Undefined/Unknown
 Note
 Proceedings title: Theory and applications of special functions: a volume dedicated to Mizan Rahman
Publisher: Springer
Place of publication: New York
ISBN: 0387242317
Editors: M.E.H. Ismail, E. Koelink  Permalink
 http://hdl.handle.net/11245/1.238153
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