Re: Summing the term...
- To: mathgroup at smc.vnet.net
- Subject: [mg38749] Re: Summing the term...
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 8 Jan 2003 04:13:18 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <avehth$mfm$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
Mathematica 4.2 say
In[]:=Sum[Binomial[2 j, j + 1] p^j, {j, 1, n}] // FullSimplify //
InputForm
Out[]= -(-1 + Sqrt[1 - 4*p] + 2*p)/(2*Sqrt[1 - 4*p]*p) -
(p^(1 + n)*Gamma[3 + 2*n]*
((1 + n)*(3 + n)*Hypergeometric2F1[1, 3/2 + n, 3 + n,
4*p] + 2*(3 + 2*n)*p*Hypergeometric2F1[2, 5/2 + n,
4 + n, 4*p]))/(Gamma[2 + n]*Gamma[4 + n])
Regards
Jens
Constantine Elster wrote:
>
> Hi All.
>
> Does anyone know if the following sum has a solution (hint of how to solve
> it is welcome too:)) ):
>
> T[n_, p_] := Sum[Binomial[2 j, j+1] p^j, {j, 1, n}]
>
> Thank you very much.
> Constantine Elster.
>
> Constantine Elster
> Computer Science Dept.
> Technion I.I.T.
> Office: Taub 411
> Tel: +972 4 8294375