Mathematica Problem

*Subject*: Mathematica Problem*From*: jack at sun.acs.udel.edu*Date*: Mon, 19 Jun 89 14:51:49 -0500*Apparently-to*: mathgroup-out at yoda.ncsa.uiuc.edu

Perhaps someone can help solve the following Mathematica problem: Given y' = y, solve using a series solution and prove that the result is E[x]. It is proving that the result is E[x] that I have not been able to do. Here is a sample session: In[1]:= Derivative[n_][y][x_]:=Derivative[n-1][y][x] In[2]:= Series[y[x],{x,0,5}] 2 3 4 5 y[0] x y[0] x y[0] x y[0] x 6 Out[2]= y[0] + y[0] x + ------- + ------- + ------- + ------- + O[x] 2 6 24 120 In[3]:= seriesbyy0[x_,n_]:=Normal[Expand[Cancel[Series[y[x],{x,0,n}]/y[0]]]] In[4]:= expseries[x_,n_]:=Sum[x^i/i!,{i,0,n}] In[5]:= seriesbyy0[x,6] 2 3 4 5 6 x x x x x Out[5]= 1 + x + -- + -- + -- + --- + --- 2 6 24 120 720 In[6]:= expseries[x,6] 2 3 4 5 6 x x x x x Out[6]= 1 + x + -- + -- + -- + --- + --- 2 6 24 120 720 In[7]:= seriesbyy0[x,100]-expseries[x,100] Out[7]= 0 As shown, I can prove the results are identical for a constant value of the argument "n", but not for general n. I realize that the identity is proven by visual inspection, but I would like to prove it by showing the identity seriesbyy0[x,n] == expseries[x,n] evaluates to true. I have tried LogicalExpand, but to no avail. Jack Seltzer jack at sun.acs.udel.edu