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I have a problem with the numerical integration in Maple. Any help or suggestion will be greatly appreciated!

 

K[1] := 1.0;
K[2] := 1;
K[3] := 0.16;
nu:=-5.92;
alpha:=8;
y:=0.01;

dF:=proc(z,y)
local k,q,h;
q:=BesselI(alpha,z)/BesselI(0.0,z);
h:=2*(K[1]*q-y)/(K[3]+(K[3]^2+4*K[2]*z^2*K[1]*q-4*K[2]*z^2*y)^(1/2));
k:=-(K[3]^2+4*K[2]*z^2*(K[1]*q-y))^(-1/2);
z^nu*h^(nu-1)*exp(-1/2/h-z^2*h/2)*k;
end proc:

Hi:

I asked Maple to evaluate (using "evalf") an infinite sum and it says (very quickly) that the answer is identically 0 (not 10^(-7)).

When I numerically  evaluate a large number of terms of the sum, the answer gets smaller as the number of terms increases, so it seems that Maple is probably correct. The fact that the answer is immediate suggest that Maple is doing some analysis rather than adding a large number of numerical values.

I'd like to...

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