Re: Taylor series expansion
- Subject: [mg2575] Re: [mg2500] Taylor series expansion
- From: moorep at MARSHALL.EDU (Phil Moore)
- Date: Tue, 21 Nov 1995 09:26:02 -0500
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
On Wed, 15 Nov 1995, Peter Joseph Onesti wrote:
>
> Hello,
>
> Can anyone tell me how I can expand in a Taylor series a function like
> Sin[constants+x^m] about x=0 for non-integer values of m? Also, how does
> one specify m to be an integer only?
>
> Thanks in advance,
> P. J. Onesti
>
>
I'm assuming that you are asking how to do it in Mathematica, not
the pencil and paper method.
There is a function called Series. I haven't looked into it very much,
but, from the examples in the book, it allows negative integer powers of x.
I wrote a function for Talyor polynomials:
taylor[func_,a_,n_] = Sum[ D[(func[x],{x,i}]/. x->a)/(i!)*(x-a)^i,{i,0,n}]
(* This is the standard formula found in books *)
This has some drawbacks. First, x cannot be defined prior to calling
taylor. Second, it does not tell you what the general term of the taylor
series is, though you can certainly call talyor[f,0,20] and try to see
the pattern.