erify, if x E R, k € N: and get by consequence: n n S k=1 k=-n e (ikx) 1 sin((n +)x) sin ( 1 cos(kx)=-=-=+ + 2 sin((n + 2)x) 2sin (2)
erify, if x E R, k € N: and get by consequence: n n S k=1 k=-n e (ikx) 1 sin((n +)x) sin ( 1 cos(kx)=-=-=+ + 2 sin((n + 2)x) 2sin (2)
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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Transcribed Image Text:Verify, if x E R, k € N:
And get by consequence:
Tip:
Use complex numbers.
• z = x+iy
n
ΙΣ
k=-n
e (ikx)
n
Σ cos(kx)=
k=1
=
sin((n + 2)x)
sin (
1
-
2
+
sin((n +)x)
2sin (2)
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