Re: Infinite sums

• To: mathgroup at smc.vnet.net
• Subject: [mg9157] Re: Infinite sums
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 16 Oct 1997 03:37:58 -0400
• Organization: University of Western Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Jonathan Arthur wrote:

> I recently typed in the following example from page 833 of the version
> 3.0 Mathematica book into version 2 of Mathematica.
>
> Sum[x^n/n!, {n, 0, Infinity}]
>
> The book says that Mathematica should simplify this to E^x However in
> version 2.0 of the program this does not work (ie it does not simplify
> the expression at all) Is this a limitation of the previous version
> that it cannot simplify infinite sums?

In Version 2, you need to load

<<Algebra`SymbolicSum`

before you enter

Sum[x^n/n!, {n, 0, Infinity}]

> I tried other sums which also simplify (ie I can do them on paper) but
> they don't simplify either.

The SymbolicSum package will help -- though I do suggest that you
upgrade to Version 3.0.  In Australia you could contact

http://www.analytica.com.au

> Any help on using Mathematica for infinte sums in general would be
> appreciated.

The DiscreteMath`RSolve` package is also relevant:

In[1]:= <<DiscreteMath`RSolve`

In[2]:= ?ExponentialGeneratingFunction
"ExponentialGeneratingFunction[eqn, a[n], n, z] gives the exponential
generating functions Sum[a[n + m] z^n / n!, {n, 0, Infinity}] for the
functions a[n] solving eqn, with independent variable n.
ExponentialGeneratingFunction[{eqn1, eqn2, ...}, {a1[n], a2[n], ...},
n, z] gives the exponential generating functions Sum[ai[n + m] z^n /
n!, {n, 0, Infinity}] for the functions ai[n] solving eqn1, eqn2, ...,
with independent variable n.  Here m denotes the least value of n such
that a[n] (or ai[n]) appears in the equation(s).

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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