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MathGroup Archive 1995

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Re: Taylor series expansion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2575] Re: [mg2500] Taylor series expansion
  • From: Phil Moore <moorep at MARSHALL.EDU>
  • Date: Tue, 21 Nov 1995 09:26:02 -0500



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.




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