Problems Epanding Sums

*To*: mathgroup at smc.vnet.net*Subject*: [mg13216] Problems Epanding Sums*From*: Alan Mahoney <mahoney at purdue.edu>*Date*: Mon, 13 Jul 1998 07:43:05 -0400*Organization*: Purdue University*Sender*: owner-wri-mathgroup at wolfram.com

I am learning Mathematica, and chose as my first project working toward a Froebenius series solution to an ODE. I have encountered a couple questions, and would appreciate any help available. I have not been able to find the info in Wolfram's FAQs. This is a simplified example. (While I normally work from a notebook, these are from the text interface for legibility) > In[1]:= y[x_] := Sum[a[k] x^k,{k,0,Infinity}] > > In[2]:= y'[x] > > k > Out[2]= Sum[D[a[k] x , x], {k, 0, Infinity}] At this point, I would like to evaluate the derivatives inside the sum. > In[3]:= % /. Sum[a_,b_] :> Sum[Evaluate[a],b] > > Sum::itform: Argument b_ at position 2 > does not have the correct form for an iterator. > > -1 + k > Out[3]= Sum[k x a[k], {k, 0, Infinity}] It worked, but it tried to evaluate "Sum[a_,b_]" before substitution. Is there a way around this? Next, in preparation for taking some x's inside the sum, I continue with > In[4]:= Normal[Series[Sin[x],{x,0,3}]] % == 0 > > 3 > x -1 + k > Out[4]= (x - --) Sum[k x a[k], {k, 0, Infinity}] == 0 > 6 > > In[5]:= Expand[%] > > 3 > x -1 + k > Out[5]= (x - --) Sum[k x a[k], {k, 0, Infinity}] == 0 > 6 > Since the product is not at the top level due to the "== 0", the product is not expanded. No problem, > In[6]:= ExpandAll[%] > > Sum::itform: Argument (ExpandAll[#1, Trig -> False, Modulus -> 0] & )[ > {k, 0, Infinity}] at position 2 > does not have the correct form for an iterator. > > Sum::itform: Argument (ExpandAll[#1, Trig -> False, Modulus -> 0] & )[ > {k, 0, Infinity}] at position 2 > does not have the correct form for an iterator. > > > Out[6]= x Sum[(ExpandAll[#1, Trig -> False, Modulus -> 0] & )[Expand[ > > k > > D[a[k] x , x]]], (ExpandAll[#1, Trig -> False, Modulus -> 0] & )[ > > 3 > > {k, 0, Infinity}]] - (x > > > Sum[(ExpandAll[#1, Trig -> False, Modulus -> 0] & )[Expand[ > > k > > D[a[k] x , x]]], (ExpandAll[#1, Trig -> False, Modulus -> 0] & )[ > > > {k, 0, Infinity}]]) / 6 == 0 Not only is this unuseful, it causes the front-ent to segmentation fault. What is the proper way to deal with this? -- Alan W. Mahoney mahoney at purdue.edu 1283 Chemical Engineering Room B5 West Lafayette, IN 47907-1283 765+494-4052