Consider the Legendre polynomials of degree n Ph(x) = Σ (-1)m 0
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:Consider the Legendre polynomials of degree n
Ph(x) = Σ (-1)m
0<m<
where n is a nonnegative integer and m = (0,1,2,... (¹ or n)).
Which of the following is wrong?
(A) Po(x) = 1.
(B) P₂(x) = (3x² - 1).
(C) P₂k (0) = (-1) 22k (k!) ², kEN.
(D) P2k+1(0) = (−1)k 22k+¹k!(k+1)!·1³
(E) ¹₁ Po(x) P₂(x) = 0.
(2n - 2m)!
2m!(nm)!(n-2m)!"
k EN.
n-2m
x"
3
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