I know that:

and also that:

Problem is: I am not able to prove the very last equality. That's all what I need.

Seeking directions/help. Thanks a bunch!

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- Mar 26th 2011, 09:32 AMpaolopiaceGamma expansion
I know that:

and also that:

Problem is: I am not able to prove the very last equality. That's all what I need.

Seeking directions/help. Thanks a bunch! - Mar 26th 2011, 12:15 PMMoo
Hello,

write the expansion for (you know, the beginning of the Taylor series... I don't remember what's the exact name)

and then for the square root, consider it as power 1/2 and make another expansion ( ) - Mar 26th 2011, 01:09 PMpaolopiace
Thanks, good idea but it seems it does not work (unless major mistakes):

Let u = 1/n. Then:

Let Then:

Which means, the second term of the resulting series is the incorrect +1/(2n) instead of the wanted -1/(4n). - Mar 26th 2011, 01:22 PMMoo
And what if you compute ? :D

- Mar 26th 2011, 01:26 PMpaolopiace
(Doh)

...thanks...