       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:=mySeries = Expand[Normal[Series[f[x, y], {x, a, 1}, {y, b, 1}]]]

Out=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:=Replace[mySeries, ex_ /; MemberQ[ex, x] && MemberQ[ex, y] -> 0, 1]

Out=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

```

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