Re: Recursion problem in SymbolicSum
- To: mathgroup at smc.vnet.net
- Subject: [mg60701] Re: Recursion problem in SymbolicSum
- From: djw1005 at cus.cam.ac.uk (D.J. Wischik)
- Date: Sun, 25 Sep 2005 02:36:11 -0400 (EDT)
- Organization: University of Cambridge, England
- References: <dh2u72$dcl$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I forgot to say: I'm running Mathematica 5.2 on Windows XP. >I was surprised to get problems (recursion limit exceeded) when executing >a symbolic sum. The terms in the sum depend on a parameter mu. When I >leave mu unspecified and calculate the sum and then substitute a numerical >value for mu, I get the right answer. When I specify mu in the sum, the >symbolic sum fails. (The sum definitely exists and is finite.) I would be >grateful if anyone could explain this behaviour. > >PoissonProb[mu_, k_] = Exp[-mu] mu^k / k!; > >Sum[PoissonProb[mu, k] (k + 1 - 9)/(k + 1), {k, 9, Infinity}] /. > {mu -> 1.05} > >[returns the answer 1.82353 * 10^(-7) as expected] > >Sum[PoissonProb[1.05, k](k + 1 - 9)/(k + 1), {k, 9, Infinity}] > >[ $RecursionLimit::reclim: Recursion depth of 256 exceeded. >$IterationLimit::itlim: Iteration limit of 4096 exceeded. >and then it returns the following. ] > >\!\(0.34993774911115527`\ \((4.298654386611213`*^-6 - > 7.999999999999789`\ \ >Hold[If[MatchQ[Numerator[SymbolicSum`InfiniteDump`expr1$214], >SymbolicSum`a$_ \ >+ SymbolicSum`b$_ /; \(! > FreeQ[SymbolicSum`a$, > K$94]\) && \(! FreeQ[SymbolicSum`b$, K$94]\)], \ >\((SymbolicSum`InfiniteDump`infinitesum[#1, K$94, 0] &)\) /@ > Expand[SymbolicSum`InfiniteDump`expr1$214], > SymbolicSum`InfiniteDump`HypergeometricSeries[ > 1, SymbolicSum`InfiniteDump`expr1$214, \ >SymbolicSum`InfiniteDump`expr2$214, K$94, 0, SymbolicSum`eps$214]]])\)\) > >Damon. >