Multi-Variate Taylor Series Expansions

*To*: mathgroup at smc.vnet.net*Subject*: [mg14718] Multi-Variate Taylor Series Expansions*From*: Tom Bell <tombell at stanford.edu>*Date*: Tue, 10 Nov 1998 01:21:08 -0500*Sender*: owner-wri-mathgroup at wolfram.com

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)

**Follow-Ups**:**Re: Multi-Variate Taylor Series Expansions***From:*Carl Woll <carlw@u.washington.edu>