use some form of technology to determine the ﬁrst four terms in the Legendre series expansion of the given function on the interval (−1,1). Plot the given function and the approximationsS1 =a0P0, S3 =a0P0+a1P1+a2P2,S5 =a0P0+a1P1+a2P2+a3P3+a4P4on the interval (−1,1). Comment on the convergence of the Legendre series to the given function for−1 < x < 1.Q. ⋄ f(x)=cosπx.

As per the question we are given the following function : f(x) = cos(πx) for x ∈ (-1, 1) And we…

Answered: use some form of technology to…

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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use some form of technology to determine the ﬁrst four terms in the Legendre series expansion of the given function on the interval (−1,1). Plot the given function and the approximations
S₁ =a₀P₀, S₃ =a₀P₀+a₁P₁+a₂P₂,

S₅ =a₀P₀+a₁P₁+a₂P₂+a₃P₃+a₄P₄

on the interval (−1,1). Comment on the convergence of the Legendre series to the given function for−1 < x < 1.

Q. ⋄ f(x)=cosπx.

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