mmalek

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16 years, 39 days

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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) ;
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