Let P, (x) be the Legendre polynomial of degree n. Show that for any function, f(x), for which the nth derivative is continuous, (- 1)" 2" n ! 1 S s) P, (x) dx = - 1y f" ) dx. S (1? – 1Y" f" (x) dx. - 1
Let P, (x) be the Legendre polynomial of degree n. Show that for any function, f(x), for which the nth derivative is continuous, (- 1)" 2" n ! 1 S s) P, (x) dx = - 1y f" ) dx. S (1? – 1Y" f" (x) dx. - 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let P, (x) be the Legendre polynomial of degree n. Show that for any
function, f (x), for which the nth derivative is continuous,
1
J f(x) Pn (x) dx
(- 1)"
2" n !
J (2 – 1y" f" (x) dx.
%3D
-1
- 1
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