2. Find the Fourier series expansion of: [o, f(1) = -1

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. Find the Fourier series expansion of:
[0,
f(r) =
-1<r<0
sin Tr,
0 < x <1
and then use it to find the values of the following infinite sum
ums:
1
1
1
(a)
1
1
15
35
4n?
+...
1
(b)
3
(-1)n+1
+
4n2 – 1
...
15
35
63
1
1
(c)
1
+
16n2 – 1
+...
15
63
143
255
1
1
1
(d)
32
(4n2 – 1)2
152
352
632
-18 -18
Transcribed Image Text:2. Find the Fourier series expansion of: [0, f(r) = -1<r<0 sin Tr, 0 < x <1 and then use it to find the values of the following infinite sum ums: 1 1 1 (a) 1 1 15 35 4n? +... 1 (b) 3 (-1)n+1 + 4n2 – 1 ... 15 35 63 1 1 (c) 1 + 16n2 – 1 +... 15 63 143 255 1 1 1 (d) 32 (4n2 – 1)2 152 352 632 -18 -18
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