Re: Recursion problem in SymbolicSum
- To: mathgroup at smc.vnet.net
- Subject: [mg60715] Re: Recursion problem in SymbolicSum
- From: Peter Pein <petsie at dordos.net>
- Date: Sun, 25 Sep 2005 02:36:27 -0400 (EDT)
- References: <dh2u72$dcl$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
D.J. Wischik schrieb: > 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. > Hi Damon, this is really strange, because Sum[Apart[PoissonProb[1.05, k]*((k + 1 - 9)/(k + 1))], {k, 9, Infinity}] returns 1.8235341181685322*^-7 For some reason Apart changes FullForm[(0.3499377491111553*1.05^k*(-8 + k))/((1 + k)*k!)] to FullForm[(0.3499377491111553*1.05^k*(-7.999999999999999 + 0.9999999999999999*k))/((1. + 1.*k)*k!)] I don't see any need to change the numbers to anything other than 8.0 and 1.0 resp. and why this error happens for mu=1.05 but not for 1.049 or 1.051. This seems to be a task for the programmers at Wolfram Research. Peter -- Peter Pein, Berlin GnuPG Key ID: 0xA34C5A82 http://people.freenet.de/Peter_Berlin/