       Re: Re: Taylor Series in R^n

• To: mathgroup at smc.vnet.net
• Subject: [mg8080] Re: [mg8065] Re: [mg8019] Taylor Series in R^n
• From: "C. Woll" <carlw at u.washington.edu>
• Date: Tue, 5 Aug 1997 03:22:47 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Bob,

Concerning the message you wrote on Taylor Series, perhaps you or somebody
else could enlighten me concerning the following behavior of Series:

f[x_,y_]:=Sin[x+y]
Series[f[x,y],{x,0,1},{y,0,1}]
Series[f[x,y],{x,0,1},{y,0,0}]
Series[f[x,y],{x,0,0},{y,0,1}]

which produces

(y+O[y^2]) + (1+O[y^2])x + O[x^2]
(y+O[y^2]) + O[x^1]
(y-y^3/6+y^5/120+O[y^7]) + O[x^1]

Note the second and third results, which are not at all what I expected or
hoped for. It seems the only time Series works properly with more than one
dependent variable, is when the order of the two variables is the same.

Carl Woll

On Mon, 4 Aug 1997 BobHanlon at aol.com wrote:

> For example, evaluate these cells:
>
> f[x_, y_, z_] := x^3 z Exp[x y] + 2 x y Log[1-z]
> Series[f[x, y, z], {x, 0, 5}, {y, 0, 5}, {z, 0, 5}]
> Series[f[x, y, z], {x, 0, 5}, {z, 0, 5}, {y, 0, 5}]
> Series[f[x, y, z], {y, 0, 5}, {x, 0, 5}, {z, 0, 5}]
> Series[f[x, y, z], {y, 0, 5}, {z, 0, 5}, {x, 0, 5}]
> Series[f[x, y, z], {z, 0, 5}, {x, 0, 5}, {y, 0, 5}]
> Series[f[x, y, z], {z, 0, 5}, {y, 0, 5}, {x, 0, 5}]
>
> Bob Hanlon
>
>

```

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