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MathGroup Archive 2005

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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
> 
> 
> 
> __________________________________________________
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> 
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


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