Re: Recursion problem in SymbolicSum

• To: mathgroup at smc.vnet.net
• Subject: [mg60703] Re: [mg60693] Recursion problem in SymbolicSum
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 25 Sep 2005 02:36:13 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Damon,

Sum likes exact terms.

PoissonProb[mu_, k_] = Exp[-mu] mu^k / k!;
Sum[PoissonProb[105/100, k](k + 1 - 9)/(k + 1), {k, 9, Infinity}]
% // N
(124072356171829 - 43417600000000*E^(21/20))/
(5734400000000*E^(21/20))
1.823534118168532*^-7

Or use NSum...

NSum[PoissonProb[1.05, k](k + 1 - 9)/(k + 1), {k, 9, Infinity}]
1.8235341173063736*^-7

David Park

From: D.J. Wischik [mailto:djw1005 at cus.cam.ac.uk]
To: mathgroup at smc.vnet.net

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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