       Re: Why are the functions different?

• To: mathgroup at smc.vnet.net
• Subject: [mg55650] Re: [mg55609] Why are the functions different?
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 1 Apr 2005 05:36:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Helge,

Use...

f1[x_] = Normal[Series[Tanh[x], {x, 0, 5}]]
f0[x_] := x - x^3/3 + (2*x^5)/15

and then everything plots properly.

Plot[f0[x], {x, -2, 2}];
Plot[f1[x], {x, -2, 2}];

By using Set instead of DelayedSet on f1, f1 is actually defined as the
series approximation. By using DelayedSet and then putting it in Plot,
without using Evaluation, Plot substitutes explicit x values into the Series
expression, which then makes no sense. For example the 'iterator' portion
then takes forms like {1.2, 0, 5} instead of {x, 0, 5} when Plot is trying
to evaluate at x = 1.2.

Now I wonder if you email address will work after I edit it.

David Park

From: Helge Stenstroem
To: mathgroup at smc.vnet.net
[mailto:helge.stenstrom.NOSPAM at NOSPAMericsson.com]

How are these two functions (f0 and f1) different? f0 can be plotted,
but f1 cannot.

f1[x_] := Normal[Series[Tanh[x], {x, 0, 5}]]
f0[x_] := x - x^3/3 + (2*x^5)/15

When evaluated like this:
f0[x]
f1[x]
they look the same.

The following gives error messages if f0 is replaced by f1.
Plot[{Tanh[z], f0[z]}, {z, -1, 1}]

(Mathematica 4.1 on Windows 2000)
--
Helge Stenström

```

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