Find the Fourier series to represent f(x): = edr in the interval -T < a < T. 2n(-1)" sinh aT T(a² + n?) sinh an 2a(-1)" sinh an f(x) = *COs nx+ •sin næ T(a? + n?) 2ra n=1 n=1 O i. f(2) = sinh an 2n(-1)" sinh aT 2a(-1)" sinh aT Σ •COS nx+ •sin na T(a² +n?) T(a² +n?) та n=1 n=1 O ii. f(2) = sinh an 2a(-1)" sinh ar 2n(-1)" sinh aT COS nx+ •sin na T(a² + n?) T(a² + n²) n=1 n=1 O iv. f(a) = sinh an 2a(-1)" sinh aT 2a(-1)" sinh aT •COS nx+ sin nx T(a² + n?) T(a² +n2) n=1 n=1 IM: IM: IM: iM:

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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Question
Find the Fourier series to represent f(a):
= ear in the interval - T <x <T.
sinh an
O i.
f (x) =
2a(-1)" sinh an
T(a? + n?)
2n(-1)" sinh aT
•COS nx+
sin nx
2na
T(a? + n?)
n=1
n=1
O i.
f (æ) =
2n(-1)" sinh an
T(a² + n²)
sinh an
2a(-1)" sinh aT
COS nx+
•sin nx
T(a² + n?)
та
n=1
n=1
O i.
f(x) =
sinh an
2a(-1)" sinh an
2n(-1)" sinh ar
•COS nx+
sin nx
T(a² + n²)
T(a? + n²)
n=1
n=1
sinh an
O iv.
f (x) =
2a(-1)" sinh aT
T(a? + n?)
2a(-1)" sinh aT
COs nx+
sin nx
T (a² +n²)
n=1
n=1
Transcribed Image Text:Find the Fourier series to represent f(a): = ear in the interval - T <x <T. sinh an O i. f (x) = 2a(-1)" sinh an T(a? + n?) 2n(-1)" sinh aT •COS nx+ sin nx 2na T(a? + n?) n=1 n=1 O i. f (æ) = 2n(-1)" sinh an T(a² + n²) sinh an 2a(-1)" sinh aT COS nx+ •sin nx T(a² + n?) та n=1 n=1 O i. f(x) = sinh an 2a(-1)" sinh an 2n(-1)" sinh ar •COS nx+ sin nx T(a² + n²) T(a? + n²) n=1 n=1 sinh an O iv. f (x) = 2a(-1)" sinh aT T(a? + n?) 2a(-1)" sinh aT COs nx+ sin nx T (a² +n²) n=1 n=1
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