(a) Assume that f(x) is function defined by -4 if -T≤ x < 0, f(x) = for 0≤x≤T. (i) Expand the function f(x) in a Fourier series.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(a) Assume that f(x) is function defined by
-7 if - <x<0,
f(x)
{
for 0≤x≤T.
(i) Expand the function f(x) in a Fourier series.
(ii) Assuming that the series in part (i) converges to f, show that
π
1
1
= 1+=
3
5
7
(b) Prove the inequality
x² + x² + ... + x²/2
( ²₁ + x₂ + ... + x n ) ²
n
n
>
Transcribed Image Text:(a) Assume that f(x) is function defined by -7 if - <x<0, f(x) { for 0≤x≤T. (i) Expand the function f(x) in a Fourier series. (ii) Assuming that the series in part (i) converges to f, show that π 1 1 = 1+= 3 5 7 (b) Prove the inequality x² + x² + ... + x²/2 ( ²₁ + x₂ + ... + x n ) ² n n >
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