1Obviously , the antiderivative of the given function ( which , in this case , turns out to be a
Hypergeometric series ) is not so easy to find . Also the integration must be carried out in a
manner in which convergence issues must be taken care of . But since here " n " is given to
be a natural number , so we need not worry about them . However a stricter condition
would have been ;
Real Part Of " n " > 1 .
I denote the original integral as " I " .
Now in the original integral , let us substitute
Here , I used two standard identities involving Gamma functions . The first one is -
which is nothing but ,
And the second one , commonly referred to as Euler ' s Reflection Formula is -
1Another thing that struck me while I pondered over the solution is that the usage of complex
integration , i . e , Contour Integration may have been an efficient way , but still , I think that would
require a high skill in Complex Analysis which I obviously lack .
23ricky tune fod diya yaar, ur posts look like as if prophet/kaymant sir are replying
tnx man
akhil ye sab syllabus me nai hai
1awesum got to noe abt tht Euler ' s Reflection Formula thnxx ricky bhaiiya
