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Re: Recursion problem in SymbolicSum


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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