Question: inconsistent output - what am I missing?


I'm new to these forums. I'm using Maple 17. What am I missing about the odd behaviour exhibited below? (the code can be copy pasted into Maple)

Suppose I define m,n,p,q as integers and x as real, then define the function h(x,m,n,p,q) below.

assume(m::integer, n::integer, p::integer, q::integer, x::real);

If I do:

int(h(x, m, n, p, q), x = -infinity .. infinity)

It says it's 0, but that's not true. The integral is not always 0 but depends on m,n,p,q ... and even Maple acknowledges this. If I do:

int(h(x, 1, 1, 1, 1), x = -infinity .. infinity)

I get -(1/2*I)/Pi ... so clearly not 0.

Also, if I do:

int(h(x, m, n, m, n), x = -infinity .. infinity)

I get -(1/2*I)/(m*Pi) ... again, not 0.

What am I missing? How can I correct this and obtain the analytic expression for int(h(x, m, n, p, q), x = -infinity .. infinity)?

Trying without the assume() causes Maple to run into issues not knowing anything about m,n,p,q.

[ Edit: I finally solved the integral on paper, see my post below if you're curious. The Maple inconsistency and wrong result explained above are still there though ]

Any help would be greatly appreciated.



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