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Re: Problems Epanding Sums

  • To: mathgroup at
  • Subject: [mg13259] Re: Problems Epanding Sums
  • From: Paul Abbott <paul at>
  • Date: Fri, 17 Jul 1998 03:17:52 -0400
  • Organization: University of Western Australia
  • References: <6oersd$guj$>
  • Sender: owner-wri-mathgroup at

Alan Mahoney wrote:

> I am learning Mathematica, and chose as my first project working toward
> a Froebenius series solution to an ODE.  

When dealing with Sums, I find that omitting the (explicit) Sum and
using the Einstein summation convention, which sums over repeated
indicies, is advantageous.  (This is, implicitly, what a human really

> (While I normally work from a notebook, these are from the text
> interface for legibility)

You could always post your Notebook too?  I really wish that this
newsgroup properly supported Notebook attachments ... :-(

For your example, we omit the Sum altogether:

	In[1]:= y[x_] := a[k] x^k
	In[2]:= y'[x]
			   -1 + k
			k x       a[k]

	In[3]:= Normal[Series[Sin[x],{x,0,3}]]%//Expand
			   k        1    2 + k
			k x  a[k] - - k x      a[k]

Using pattern-matching and Collect, we obtain the recurrence relation
that you are after:

	In[4]:= %/.c_ x^(k+n_.):>(c x^(k+n)/.k->k-n)
			  1            k                k
			-(-) (-2 + k) x  a[-2 + k] + k x  a[k]

	In[5]:= Collect[%,x,Simplify]
			  1   k
			-(-) x  ((-2 + k) a[-2 + k] - 6 k a[k])

Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at  AUSTRALIA                   

            God IS a weakly left-handed dice player

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