A set of orthogonal polynomials induced by a given orthogonal polynomial
نویسندگان
چکیده
منابع مشابه
A Set of Orthogonal Polynomials Induced by a Given Orthogonal Polynomial
Given an integer n ~ 1, and the orthogonal polynomial1rn (· ; du) of degree n relative to some positive measure du, the polynomial system "induced" by 1rn is the system of orthogonal polynomials {7rk,n} corresponding to the modified measure dUn = 1r~du. Our interest here is in the problem of determining the coefficients in the three-term recurrence relation for the polynomials 7rk,n from the re...
متن کاملOrthogonal Polynomials and Polynomial Approximations
3.1.1. Existence and uniqueness. Our immediate goal is to establish the existence of a sequence of orthogonal polynomials. Although we could, in principle, determine the coefficients a j of pn in the natural basis by using the orthogonality conditions (3.1.2), it is computationally advantageous to express pn in terms of lower-order orthogonal polynomials. Let us denote Pn := span { 1, x, x, · ·...
متن کاملOn orthogonal polynomials obtained via polynomial mappings
Let (pn)n be a given monic orthogonal polynomial sequence (OPS) and k a fixed positive integer number such that k ≥ 2. We discuss conditions under which this OPS originates from a polynomial mapping in the following sense: to find another monic OPS (qn)n and two polynomials πk and θm , with degrees k and m (resp.), with 0 ≤ m ≤ k − 1, such that pnk+m(x) = θm(x)qn(πk(x)) (n = 0, 1, 2, . . .). In...
متن کاملExplicit Orthogonal Polynomials for Reciprocal Polynomial Weights
Let S be a polynomial of degree 2n + 2, that is, positive on the real axis, and let w = 1/S on (−∞,∞). We present an explicit formula for the nth orthogonal polynomial and related quantities for the weight w. This is an analogue for the real line of the classical Bernstein-Szegő formula for (−1, 1). 1. The result The Bernstein-Szegő formula provides an explicit formula for orthogonal polynomial...
متن کاملSolving singular integral equations by using orthogonal polynomials
In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Aequationes Mathematicae
سال: 1993
ISSN: 0001-9054,1420-8903
DOI: 10.1007/bf01834006