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
djmp at earthlink.net
http://home.earthlink.net/~djmp/
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.