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[1], Derivative[1][f][1], Derivative[1][f][1]/2 + Derivative[2][f][1]/ 2, Derivative[1][f][1]/6 + Derivative[2][f][1]/2 + Derivative[3][f][1]/6}, 0, 4, 1] The expansion point of the second series has been chosen correctly. Exp[0]==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 ? >