       Re: Composition of series

• To: mathgroup at smc.vnet.net
• Subject: [mg65349] Re: Composition of series
• From: dh <dh at metrohm.ch>
• Date: Tue, 28 Mar 2006 04:05:13 -0500 (EST)
• References: <e08ko1\$4c0\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
you will agree that a series can only have one expansion point.
Therefore, if we compose seires we may not simply replace the variable
of one series by a second series. However, if we do a complete
expansion, everything works just fine: E.g.:

x1 = Series[Exp[x], {x, 0, 3}]
x2 = Series[f[x1], {x, 0, 3}]
gives (InputForm):
SeriesData[x, 0, {f, Derivative[f],
Derivative[f]/2 + Derivative[f]/
2, Derivative[f]/6 +
Derivative[f]/2 +
Derivative[f]/6}, 0, 4, 1]
The expansion point of the second series has been chosen correctly.
Exp==1. Therefore, f must be expanded around 1.

However, if you do it the wrong way:
x1 = Series[Exp[x], {x, 0, 3}]
x2 = Series[f[xx], {xx, 0, 3}] /. xx -> x1
then you get the error you mentioned.

Daniel

Geico Caveman wrote:
> I am trying to compose two series with Mathematica :
>
> One is f1(x) = ...
>
> The other is x(y) = ...
>
> ComposeSeries quits complaining that the expansion point of the first series
> is different from the constant term of the second series
> (ComposeSeries::scmp). What I am really trying to do here is to express f
> (x) as a series in Log[x] (x is strictly greater than zero), so the second
> series is simply the series expansion of Exp[y].
>
> Mathematically, what is the problem with even attempting this operation ?
> Can't I replace x by log(z) in the first series, no matter what ?
>

```

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