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Question: Why summation is not correct for Charlier

Question:Why summation is not correct for Charlier

ComputerUser 535 Maple
December 16 2012
0

restart;
with(SumTools):
an := -n+L;
bn := -x+L;
gen := Summation(Product(an, L=0..k-1)*Product(bn, L=0..k-1)/k!*(-1/a)^k, k=0..infinity);
genfun1 := subs(a=z,simplify(gen));
genfun2 := exp(z)*(1-(z/mu))^x;

 

correct is genfun2

but using famous hypergeom of charlier written in many books and papers, it can not summation to a correct generating function
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