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