New generating functions for Gegenbauer polynomials
نویسندگان
چکیده
منابع مشابه
Tutte polynomials of wheels via generating functions
We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
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In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials. Specializations of generating functions are accomplished throu...
متن کاملtutte polynomials of wheels via generating functions
we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.
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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...
متن کاملUltraspherical Type Generating Functions for Orthogonal Polynomials
We characterize, up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. 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 positivity condit...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1996
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00237-5