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A strange bug

mmalek 24
January 11 2009
0
Let f(y,θ)=y ∗ exp(−y) ∗ cos(k ∗ y ∗ cos θ). The double integrale, first over θ, from 0 to π, and then over y, from 0 to infinity, is equal to π / (1 + k^2)^(3/2) (see, Gradshteyn and Ryzhik, 6.623.2).

Maple is doing well, already in version 7 (my very first verison). You can check this by issuing the following commads
f:= cos(k ∗ y ∗ cos θ)/Pi :
i1 := int(f , θ = 0..Pi) :
i2 := int(y ∗ exp(−y) ∗ i1, y = 0..infinity) ;

Now suppose that for some reason we whish to specify k, before going to the inegration procedures. This can be of the form : assume(k>0), or simply
k = a number, for exemple k=2. The result is quite surprising :

Maple 7, Maple 9, Maple 9.5 : No answer
Maple 10, Maple 11, Maple 12 : π / sqrt(1 + k^2), so if we set k=2, we find π / sqrt(5), which is wrong.
integral infinity procedure

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