Asymptotic behaviour of Stieltjes polynomials for ultraspherical weight functions
نویسندگان
چکیده
منابع مشابه
Ultraspherical Type Generating Functions for Orthogonal Polynomials
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...
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 کاملInterlacing and asymptotic properties of Stieltjes polynomials
Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials have been studied since the 1830’s, beginning with Lamé in his studies of the Laplace equation on an ellipsoid, and in an ever widening variety of applications since. In this paper we show how the zeros of Stieltjes polynomials are distributed and present two new interlacin...
متن کاملStieltjes polynomials and related quadrature formulae for a class of weight functions
Consider a (nonnegative) measure dσ with support in the interval [a, b] such that the respective orthogonal polynomials, above a specific index `, satisfy a three-term recurrence relation with constant coefficients. We show that the corresponding Stieltjes polynomials, above the index 2` − 1, have a very simple and useful representation in terms of the orthogonal polynomials. As a result of thi...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1995
ISSN: 0377-0427
DOI: 10.1016/0377-0427(95)00107-7