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+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)=x(1−x2)ex

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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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)=x(1−x2)ex

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