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MathGroup Archive 2005

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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.



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