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.
>

```

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