[seqfan] Proof or counter sample needed

[Richard Mathar]

> From seqfan-bounces at list.seqfan.eu  Mon Oct 27 00:50:49 2008
> Date: Mon, 27 Oct 2008 00:19:31 +0100
> From: Artur <grafix at csl.pl>
> To: grafix at csl.pl
> Cc: seqfan at yahoogroups.com,
>         Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: Re: [seqfan] Proof or counter sample needed
> 
> Hypergeometric2F1[1/5, 4/5, 1/2, 3/4]=GoldenRatio=(1+Sqrt[5])/2
> Artur

This is the case n=3/5, z^2=3/4 of equation 9.121.32 of the
book by GradStein and Ryshik, namely
F( (1+n)/2, (1-n)/2 ; 1/2 ; z^2) = [cos(n*arcsin(z))]/sqrt(1-z^2) 
where arcsin[sqrt(3)/2]=Pi/3, see A019863.