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

In:= Normal[Series[Sin[x],{x,0,3}]]%//Expand
Out=
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:= %/.c_ x^(k+n_.):>(c x^(k+n)/.k->k-n)
Out=
1            k                k
-(-) (-2 + k) x  a[-2 + k] + k x  a[k]
6

In:= Collect[%,x,Simplify]
Out=
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
____________________________________________________________________

```

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