Re: general nth term of series

*To*: mathgroup at smc.vnet.net*Subject*: [mg62992] Re: general nth term of series*From*: Peter Pein <petsie at dordos.net>*Date*: Sat, 10 Dec 2005 06:03:02 -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. > ... Hi Ash, SeriesTerm[(1 - 2*x*u + u^2)^(-1/2), {u, 0, n}] gives LegendreP[n,x] without any Gammas in Version 5.1 Use SeriesTerm with care. It is quite buggy for general n: Series[Sin[x]/(1 + x), {x, 0, 5}]//Normal --> x - x^2 + (5*x^3)/6 - (5*x^4)/6 + (101*x^5)/120 SeriesTerm[Sin[x]/(1 + x), {x, 0, 5}] --> 101/120 is OK, but: SeriesTerm[Sin[x]/(1 + x), {x, 0, n}] /. n -> 5 --> Sqrt[Pi/2]*BesselJ[1/2, 1] N[120 %] --> 100.977 _Incidentally_ almost good... SeriesTerm gives for this example (-(-1)^n)*Sqrt[Pi/2]*BesselJ[1/2, 1] as coefficient of x^n. :-\ Peter