If a Gaussian quadrature formula n [ f(x)w(x) dx = [A₁f(xi) a i=0 holds for all f(x) = P2n+1, show that the polynomial [(x − x) is orthog- onal to Pn on [a, b] with respect to w.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.5: Systems Of Linear Equations In More Than Two Variables
Problem 43E
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If a Gaussian quadrature formula
n
[ f(x)w(x) dx = [A₁f(xi)
a
i=0
holds for all f(x) = P2n+1, show that the polynomial Io(x − x;) is orthog-
onal to Pn on [a, b] with respect to w.
Transcribed Image Text:If a Gaussian quadrature formula n [ f(x)w(x) dx = [A₁f(xi) a i=0 holds for all f(x) = P2n+1, show that the polynomial Io(x − x;) is orthog- onal to Pn on [a, b] with respect to w.
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