2. Prove that there exists a polynomial p(x) such that and 2π * P(a)sin(a)dx = 2π 1 | S*"* P(z)sin(n.z),de| < 1,000,000 dx Hint: cos(-y)-cos(x+y) = sin(x) sin(y). ( 2 for n = 2, 3, 4, ...
2. Prove that there exists a polynomial p(x) such that and 2π * P(a)sin(a)dx = 2π 1 | S*"* P(z)sin(n.z),de| < 1,000,000 dx Hint: cos(-y)-cos(x+y) = sin(x) sin(y). ( 2 for n = 2, 3, 4, ...
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:2. Prove that there exists a polynomial p(x) such that
2π
[*²* p(x)sin(x)dx = 7
T
and
2π
1
1,000,000
Hint: cos(-y)-cos(x+y)
2
=
p(r)sin(nz)dz <
sin(x)sin(y). (
for n = 2, 3, 4, ...
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