Re: series expansions in two variables problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg39535] Re: series expansions in two variables problem*From*: jf.alcover at bdpme.fr (jf alcover)*Date*: Sat, 22 Feb 2003 03:37:30 -0500 (EST)*References*: <b329vc$b2q$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

mc799 at ic.ac.uk (Martin) wrote in message news:<b329vc$b2q$1 at smc.vnet.net>... > hi, > I'm expanding an expression in two variables (sigma and epsilon, say), > but am having trouble persuading Mathematica to chuck away terms of > form epsilon*sigma. [...] Martin, I don't know if it's possible to get rid of the x*y terms in an expansion such as Series[f[x,y],...] at order 1, if you keep it in SeriesData form, but I have tried to do so in Normal Form and it seems to work fine this way : (everything in InputForm) In[52]:=mySeries = Expand[Normal[Series[f[x, y], {x, a, 1}, {y, b, 1}]]] Out[52]=f[a, b] - b*Derivative[0, 1][f][a, b] + y*Derivative[0, 1][f][a, b] - a*Derivative[1, 0][f][a, b] + x*Derivative[1, 0][f][a, b] + a*b*Derivative[1, 1][f][a, b] - b*x*Derivative[1, 1][f][a, b] - a*y*Derivative[1, 1][f][a, b] + x*y*Derivative[1, 1][f][a, b] In[53]:=Replace[mySeries, ex_ /; MemberQ[ex, x] && MemberQ[ex, y] -> 0, 1] Out[53]=f[a, b] - b*Derivative[0, 1][f][a, b] + y*Derivative[0, 1][f][a, b] - a*Derivative[1, 0][f][a, b] + x*Derivative[1, 0][f][a, b] + a*b*Derivative[1, 1][f][a, b] - b*x*Derivative[1, 1][f][a, b] - a*y*Derivative[1, 1][f][a, b] ( The term x*y*... has been cancelled ) Hoping this could help, jfa