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 ____________________________________________________________________