φιλ = Σ m=3,5,7.... (2a ) sin (mm) π? ᾖ 2mat το (1 - m2))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Could you explain how we expanded the sum ? Why m got out of the sum as a constant?
Transcribed Image Text:=
2
a
=
=
91¹ =
2
√² (
a
4maa
π² ħ²
4maa
π² ħ²
24 ) sin (
Σ
a
π² ħ²
2ma²
m=3,5,7....
ħ²
(sin (³x) +
a
ma
=√√() (sin (²x) -
:)
Therefore, the first three terms are
МП
2
(1 - m²))
-1
-1
·) (193° + √2/545° +1=4947° + ....)
43
1-25
4 sin (5x) + — sin (7x) + ....)
-1
-48
-24
Pm0
sin (2x) +
π² ħ²
sin (²5x) + ...)
a
ma
) (sin ( ³7x) — — sin ( 5x) + ½-sin (77x) + ...).
-
Expert Solution
Step 1
It is given that:
We have to expand the given sum.
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Solved in 5 steps
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