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November 11th, 2010, 03:16 AM   #1
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Series computation with residue theory!

[color=#000000]Compute with the help of complex analysis the series .[/color]
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November 11th, 2010, 01:22 PM   #2
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Re: Series computation with residue theory!

[color=#000000]A hint:
Take the function and then the contour integral over the circle with radius with and center .[/color]
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November 13th, 2010, 08:38 AM   #3
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Re: Series computation with residue theory!

[color=#000000]The function has a simple pole in every single with inside the circle mentioned above which we name . We will use the formula
. For the left side of the boxed equation we have,

.

Letting we take the result,

.

The line integral goes to zero as n goes to infinity because is bounded , it can be proved easily.[/color]
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