[Date Index] [Thread Index] [Author Index]

Re: general nth term of series

• To: mathgroup at smc.vnet.net
• Subject: [mg63057] Re: general nth term of series
• From: Peter Pein <petsie at dordos.net>
• Date: Sun, 11 Dec 2005 22:25:35 -0500 (EST)
• References: <dnbmun$5qm$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

N00dle schrieb:
> Thanks Carl and Daniel, for pointing out the
> SeriesTerm function from the RSolve package. 
> 
> However, my input got screwed up in copy paste. The
> function that I had intended was the generating
> function for Legendre polynomials. 
> 
> G[u_,x_]=(1 - 2*x*u + u^2)^(-1/2)
> 
> And the nth term of which, indeed gives me the
> Legendre Polynomials in terms of Gamma function. I am
> impressed.
> 
> How can I decompose this result into two seperate ones
> for even and odd values of n. So as to see the things
> in a more familiar form using factorials.
> 
> Ash
> 
> 
> 
> __________________________________________________
> Do You Yahoo!?
> Tired of spam?  Yahoo! Mail has the best spam protection around 
> http://mail.yahoo.com 
> 
Hi Ash,

I guess you mean

Simplify[SeriesTerm[G[u,x],{x,0,n},Assumptions->{}],n>=0]
--> (u^n*(1 + u^2)^(-1/2 - n)*Binomial[2*n, n])/2^n