Re: Multi-Variate Taylor Series Expansions

*To*: mathgroup at smc.vnet.net*Subject*: [mg14735] Re: [mg14718] Multi-Variate Taylor Series Expansions*From*: me <me at talmanl1.mscd.edu>*Date*: Wed, 11 Nov 1998 17:53:39 -0500*Sender*: owner-wri-mathgroup at wolfram.com

One must use a trick to obtain multivariate Taylor polynomials. Try Normal[Series[f[x + t h, y + t k], {t, 0, 3}]] /. t -> 1 --Lou Talman Department of Mathematical and Computer Sciences Campus Box 38 Metropolitan State College of Denver PO Box 173362 Denver CO 80217-3362 http://clem.mscd.edu/~talmanl > Date: Tue, 10 Nov 1998 01:21:08 -0500 > From: Tom Bell <tombell at stanford.edu> To: mathgroup at smc.vnet.net > To: mathgroup at smc.vnet.net > Subject: [mg14735] [mg14718] Multi-Variate Taylor Series Expansions > Mime-Version: 1.0 > > > Is there a function in Mathematica that will do multi-variate Taylor > series > > expansions? For example, suppose I have > > function = F(x + dx, t + dt) > > then the expansion to second order about (x,t) should look something > like > > expansion = F(x,t) + dx D(F,x) + dt D(F,t) + (1/2) dx^2 D(F,{x,2}) + > > dx dt D(F,{x,t}) + (1/2) dt^2 D(F,{t,2}) + O(dx^3) + O(dt^3) > > The situation gets a little more complicated: the function may look like > > F(x + G(x + dx, t + dt), t + dt) and so on, so that the expansion should > be > > recursive. After expanding F, the function should keep going back and > expending G until no > > further expansions can be done. > > Please reply to tombell at stanford.edu, and thanks in advance for your > help. > > ---------------------------------------------------------------- > Thomas (Tom) Bell > Gravity Probe-B, H.E.P.L. tombell at stanford.edu > Stanford University 136D Escondido Village > Stanford, CA > 94305-4085 Stanford, CA 94305 650/725-6378 (o) > 650/497-4230 (h) 650/725-8312 (fax) >