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/

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