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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
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