Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1998
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1998

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Problems Epanding Sums

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13259] Re: Problems Epanding Sums
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 17 Jul 1998 03:17:52 -0400
  • Organization: University of Western Australia
  • References: <6oersd$guj$12@dragonfly.wolfram.com>
  • Sender: owner-wri-mathgroup at wolfram.com

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
does).  

> (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]
	Out[2]=
			   -1 + k
			k x       a[k]

	In[3]:= Normal[Series[Sin[x],{x,0,3}]]%//Expand
	Out[3]=
			   k        1    2 + k
			k x  a[k] - - k x      a[k]
			            6

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)
	Out[4]=
			  1            k                k
			-(-) (-2 + k) x  a[-2 + k] + k x  a[k]
			  6

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

Cheers,
	Paul 
 
____________________________________________________________________ 
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 physics.uwa.edu.au  AUSTRALIA                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


  • Prev by Date: Re: Re: coordinate transformation
  • Next by Date: Re: Re: Corrupt Mathematica Notebooks
  • Previous by thread: Problems Epanding Sums
  • Next by thread: symbolized symbol in LHS of function