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For , we have where is Euler's Beta function, hence .
Since everything is positive, we may interchange sum and integral:
Now, we can apply usual methods; Maple gives the value .
Last edited by Laurent; Apr 21st 2010 at 04:17 PM.
Reason: Deleted a wrong contour integration proof (integrals on sides don't cancel)
Great! My solution as well.
Originally Posted by Bruno J. Great! My solution as well. I'd be interested to see if there is a method by inverting the series expansion for arcsine.
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