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>