Re: Multiplying Polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg117965] Re: Multiplying Polynomials
- From: Dana DeLouis <dana.del at gmail.com>
- Date: Wed, 6 Apr 2011 05:12:41 -0400 (EDT)
On Apr 5, 6:44 am, Bob Hanlon <hanl... at cox.net> wrote:
> The first argument to FindGeneratingFunction is the list of the coefficients, not a list of the terms.
> n = 4;
> t = a^Range[0, n]
> {1, a, a^2, a^3, a^4}
>
> gf = FindGeneratingFunction[t, x]
> 1/(1 - a*x)
Thanks everyone for the reminder that FindGeneratingFunction uses a list of coefficients, and not the terms. (ie do not include the =91x term from the examples.)
I'll try to redeem myself. One workaround I remember using in the past is the use of an undefined veritable and setting it to 1.
For example, if you had the following sequence, and can't figure out a list of coefficients:
t = {1, a x^2, (a^2 x^4)/2, (a^3 x^6)/6, (a^4 x^8)/24, (a^5 x^10)/120}
I believe one can use an undefined veritable, and set it to 1.
gf=FindGeneratingFunction[t,z]/.z->1
E^(a x^2)
Series[gf,{x,0,10}]//Normal
1 + a x^2 + (a^2 x^4)/2 + (a^3 x^6)/6 + (a^4 x^8)/24 + (a^5 x^10)/120
which checks.
Another example:
t={x^4/a, x^5, a x^6, a^2 x^7, a^3 x^8, a^4 x^9};
gf=FindGeneratingFunction[t,z]/.z->1
-(x^4/(a (a x-1)))
Series[gf,{x,0,9}]//Normal
x^4/a + x^5 + a x^6 + a^2 x^7 + a^3 x^8 + a^4 x^9
which checks.
And the original problem:
t={1,a x,a^2 x^2,a^3 x^3};
gf=FindGeneratingFunction[t,z]/.z->1
1/(1-a x)
Thanks everyone for the reminder. :>o
= = = = = = = = = =
Dana DeLouis
Mac, Ver 8=