       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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```

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