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