Orthogonalize {1, t, t²} in P₂ (R) with 1 (f, 9) = ["ª, f(x)g(x) dx. -1 Then normalize each one so that its graph passes through (1,1). These are the first three Legendre polynomials.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 28E
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Orthogonalize {1, t, t²} in P₂ (R) with
2
1
(f,g) = [*, f(x)g(x) dx.
-1
Then normalize each one so that its graph passes through (1,1). These are the first three Legendre
polynomials.
"
"
2
}
Transcribed Image Text:Orthogonalize {1, t, t²} in P₂ (R) with 2 1 (f,g) = [*, f(x)g(x) dx. -1 Then normalize each one so that its graph passes through (1,1). These are the first three Legendre polynomials. " " 2 }
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