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Re: Composition of series

• To: mathgroup at smc.vnet.net
• Subject: [mg65350] Re: [mg65337] Composition of series
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Tue, 28 Mar 2006 04:05:14 -0500 (EST)
• References: <200603271156.GAA04167@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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 ?

Can't you just do:

f[Exp[y]]+O[y]^5 /. y->Log[x]

For example:

In[11]:=
Sin[Exp[y]] + O[y]^3 /. y -> Log[x]

Out[11]=
Sin[1]+Cos[1] Log[x]+1/2 (Cos[1]-Sin[1]) (Log[x])^2+(O[Log[x]])^3

Carl Woll
Wolfram Research

• References:
  • Composition of series
    • From: Geico Caveman <spam@spam.invalid>