Jacobi functions as limit cases of q-ultraspherical polynomials
نویسندگان
چکیده
منابع مشابه
On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving (q-)Hahn polynomials, little q-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from q-Racah to Racah polynomials ar...
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We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...
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متن کاملUltraspherical Type Generating Functions for Orthogonal Polynomials
We characterize, under some technical assumptions and up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. Our method is based on differential equations and the obtained measures are particular Beta distributions. We actually recover the free Meixner family of probability distributions so that our met...
متن کاملA second addition formula for continuous q-ultraspherical polynomials
This paper provides the details of Remark 5.4 in the author’s paper “Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group”, SIAM J. Math. Anal. 24 (1993), 795–813. In formula (5.9) of the 1993 paper a two-parameter class of Askey-Wilson polynomials was expanded as a finite Fourier series with a product of two 3phi2’s as Fourier coefficients. The proof given there use...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1990
ISSN: 0022-247X
DOI: 10.1016/0022-247x(90)90026-c