Given then compute

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- Dec 8th 2009, 07:53 AMKrizalidSeries
Given then compute

- Dec 8th 2009, 09:40 AMPaulRS
We have: when

Now integrate:

Hence: for . it follows then, by substituting that

Because we have: - Jan 26th 2011, 07:33 PMKrizalid
when i saw first this problem, i got beaten, but i tried later, and i think i consider my solution a bit brute. (Evilgrin)

- Jun 29th 2011, 05:59 PMTheCoffeeMachineRe: Series
I propose a solution using Cauchy multiplication. Consider:

Now consider the inner sum in the following way:

Where on the third step we shifted the index for the sum on the right.

Your sum is a special case of the above and occurs when x = 1/2.