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.
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
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 53E
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7517b38-af2d-4634-9337-add95a3fbd4d%2F144764e6-7012-4a8a-9167-8a37441db119%2Fclkv73l_processed.png&w=3840&q=75)
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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