       Taylor Series Expansions

• To: mathgroup at smc.vnet.net
• Subject: [mg32372] Taylor Series Expansions
• From: Joe Helfand <jhelfand at wam.umd.edu>
• Date: Wed, 16 Jan 2002 03:31:08 -0500 (EST)
• Organization: University of Maryland College Park
• Sender: owner-wri-mathgroup at wolfram.com

```Wow!

I have definitely come to the right place.  Thanks for all the
responses.  Using the Map built in function solved my problem (it still
took a bit, so you can imagine what I was dealing with).  Here is
something else which I have wasted some time on not knowing as much
about Mathematica as I should.  It has to do with multi-variable Taylor
series expansion.  Mathematica has a built in Series function.  But when
you use this for multi-variable functions, it doesn't do quite what I'd
expect.  Let's say I have a function for two fariables, and I want to
expand to 2nd order.  When I use Series, it expands each varible to
second order, but includes the cross terms, which I want to belong to a
4th order expansion.  For example:

In:=
Normal[Series[Exp[x y], {x, 0, 2}, {y, 0, 2}]]

Out=
\!\(1 + x\ y + \(x\^2\ y\^2\)\/2\)

But what I really want is just 1 + x y, where if I go to fourth order,
then I'll take the x^2 y^2 / 2.  I had to take some time to write some
sloppy Taylor series expansion functions that did what I wanted.  Is
there a way to get around this problem or do you have any suggestions?

Thanks Again,
Joe

```

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