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2. Use Parseval's formula and a suitable Fourier series to sum 2n=1 (2n–1)? · 1 Hint: Look at Table 5.1. in the lecture notes.

2. Use Parseval's formula and a suitable Fourier series to sum 2n=1 (2n–1)? · 1 Hint: Look at Table 5.1. in the lecture notes.

Advanced Engineering Mathematics
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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2. Use Parseval's formula and a suitable Fourier series to sum 2n=1 (2n–1)? · 1 Hint: Look at Table 5.1. in the lecture notes.
Transcribed Image Text:2. Use Parseval's formula and a suitable Fourier series to sum 2n=1 (2n–1)? · 1 Hint: Look at Table 5.1. in the lecture notes.
Table 5.1: Examples of Fourier series f(x) žao + (an cos nx + b, sin nx) n=1 sin nx i) x, 0<x < T E(-1)n+1! n n=1 sin nx ii) (T – x), 0< x < T n n=1 iii) T, 0<x < T sin(2n – 1)x 2n – 1 n=1 2(-1)a-1 Cos(2n – 1)x 2n – 1 0 <x < T iv) (-7, T < x < T n=1 Cos na v) (T? – 3x?), 0 < x < T E(-1)--1! n2 n=1 Cos nx vi) (T – 2)? – 7?, 0< x < a n2 n=1 .cos(2n – 1)x (2n – 1)2 vii) 7(T – 2), 0< x < ™ n=1 2(-1)a-1 sin(2n – 1)x (2n – 1)2 0 < x < }T viii) {#(7 – x), T< x < a | n=1
Transcribed Image Text:Table 5.1: Examples of Fourier series f(x) žao + (an cos nx + b, sin nx) n=1 sin nx i) x, 0<x < T E(-1)n+1! n n=1 sin nx ii) (T – x), 0< x < T n n=1 iii) T, 0<x < T sin(2n – 1)x 2n – 1 n=1 2(-1)a-1 Cos(2n – 1)x 2n – 1 0 <x < T iv) (-7, T < x < T n=1 Cos na v) (T? – 3x?), 0 < x < T E(-1)--1! n2 n=1 Cos nx vi) (T – 2)? – 7?, 0< x < a n2 n=1 .cos(2n – 1)x (2n – 1)2 vii) 7(T – 2), 0< x < ™ n=1 2(-1)a-1 sin(2n – 1)x (2n – 1)2 0 < x < }T viii) {#(7 – x), T< x < a | n=1
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