question

*To*: mathgroup at smc.vnet.net*Subject*: [mg75255] question*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 22 Apr 2007 05:10:39 -0400 (EDT)

Hello. In Mathematica 5.2 I got In[73]:= Integrate[1/Sqrt[Sin[u]], {u, 0, Pi/2}] Out[73]= 2*EllipticF[Pi/4, 2] The result ic correct as a numerical integration indicates. In[74]:= {Chop[N[%]], NIntegrate[1/Sqrt[Sin[u]], {u, 0, Pi/2}]} Out[74]= {2.6220575244897986, 2.622057554312378} It can be proved that the definite integral under discussion is given by Gamma[1/4]^2/(2*Sqrt[2*Pi]). In[75]:= N[Gamma[1/4]]^2/(2*Sqrt[2*Pi]) Out[75]= 2.6220575542921196 Can somebody point me out a way to show that the Gamma[1/4]^2/(2*Sqrt[2*Pi]) is equal to 2*EllipticF[Pi/4, 2] or/and a series of steps from taking from the latter to the former and vice versa? Thanks Dimitris

**Follow-Ups**:**Re: question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>