       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

```

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