Please help me with the below question. Consider the Legendre polynomials of degree nPh(x) = Σ (1)m0

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Answered: Consider the Legendre polynomials of…

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Advanced Math

Consider the Legendre polynomials of degree n Ph(x) = Σ (1)m 0

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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Question

Please help me with the below question.

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 NOT correct?
(A) P₁(x) = x.
(B) P3(x) = (5x³ – 3x).
(C) P2k (0) = (-1)k_(2k)!
(D) P2k+1(0) = 0, kEN.
(E) ₁ P₁(x) P3(x) dx = 0.
(2n - 2m)!
2m!(nm)!(n-2m)!
KEN.
n-2m

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