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MathGroup Archive 2000

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Re: I do not understand

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25435] Re: [mg25381] I do not understand
  • From: David Withoff <withoff at wolfram.com>
  • Date: Sun, 1 Oct 2000 02:44:20 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

> Hello,
> 
> ySer=Series[y[t],{t,0,3}]
> 
> If I apply this rule like this
> (y[t]+y'[t])/.y[t]->ySer
> both y[t] and y'[t] changes appropriately
> 
> If I apply
> y'[t]/.y[t]->ySer
> nothing happens
> 
> Why is that?

Because combining series expansions with other functions automatically
causes expansions of those other functions.  For example:

In[1]:= expr = Series[Exp[x], {x, 0, 3}]

                 2    3
                x    x        4
Out[1]= 1 + x + -- + -- + O[x]
                2    6

In[2]:= Cos[x] + x expr

                 2    3      4
                x    x    5 x        5
Out[2]= 1 + x + -- + -- + ---- + O[x]
                2    2     24

The operation (y[t]+y'[t])/.y[t]->ySer does not make a
substitution in y'[t], but adding ySer to y'[t] causes y'[t]
to be expanded.

Dave Withoff
Wolfram Research


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