Re: Series problem
- To: mathgroup at smc.vnet.net
- Subject: [mg4133] Re: [mg4084] Series problem
- From: Allan Hayes <hay at haystack.demon.co.uk>
- Date: Fri, 7 Jun 1996 02:06:13 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Tommy Nordgren <f85-tno at telesto.nada.kth.se>
[mg4084] Series problem
Writes
>I want to expand the Cosine only in the expression:
>Cos[b x] Exp[-x^2]/(k^2+x^2) into a taylor series around 0.
>Computing the series in terms of x don't work, because the
>exponetial and the divisor will be expanded as well, when the
series >of the Cosine is multiplied by the other factors.
Tommy,
You might like to try
Normal[Series[Cos[b x],{x,0,5}]] Exp[-x^2]/(k^2+x^2)
2 2 4 4
b x b x
1 - ----- + -----
2 24
-----------------
2
x 2 2
E (k + x )
The problem arises since
Series[Cos[b x],{x,0,5}]
2 2 4 4
b x b x 6
1 - ----- + ----- + O[x]
2 24
is a SeriesData object, not a series:
%//InputForm
SeriesData[x, 0, {1, 0, -b^2/2, 0, b^4/24}, 0, 6, 1]
When this is multiplied by the other terms, Mathematica , as you
observe, takes the series for the whole expression - the assumption
being that you wish to work to 0[x] ^5.
Normal changes SeriesData to an ordinary series.
Allan Hayes
haystack.demon.co.uk
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