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Re: question

• To: mathgroup at smc.vnet.net
• Subject: [mg75282] Re: [mg75255] question
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 23 Apr 2007 05:44:50 -0400 (EDT)
• References: <200704220910.FAA20298@smc.vnet.net>

On 22 Apr 2007, at 18:10, dimitris wrote:

> 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?
>

I can't see how to do this but I can at least show that this is  
equivalent to the following curious formula for Pi:

Pi == Gamma[1/4]^4/(16*EllipticK[1/2]^2)

So if one can prove (or find somewhere a proof) of this formula then  
one will also obtain your derivation.

Andrzej Kozlowski

• References:
  • question
    • From: dimitris <dimmechan@yahoo.com>