Let a not be an integer, and f (x) = cos ax, x E (-7, 7] Extend f to PC (27). Show that 1 2 cot aT = - 1 n² – a? | and 1 CSc AT = (-1)" n2 n=1

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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Let a not be an integer, and
f (x) = cos ax, x E [-n, n]
Extend f to PC (2ñ).
Show that
1 2
1
cot at
n2 – a?
n=1
and
1
CSC AT =
(-1)*
|
- -X
n2 – a?
n=1
||
Transcribed Image Text:Let a not be an integer, and f (x) = cos ax, x E [-n, n] Extend f to PC (2ñ). Show that 1 2 1 cot at n2 – a? n=1 and 1 CSC AT = (-1)* | - -X n2 – a? n=1 ||
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