Hi everyone!

I wander whether maple can solve the integral of trigonometric series with parametal N, the number of sereis, and how. The formation is showed as below. N is a variable and 'm' belongs to 'k', 'n' belongs to 'l'.

A := int(int(sum(sum(cos(2*k*Pi*x/a)*(1-cos(2*l*Pi*y/b))*(1-cos(2*m*Pi*x/a))*(1-cos(2*n*Pi*y/b)), k = 1 ..N), l = 1 .. N), x = 0 .. a), y = 0 .. b)

orthogonality codition 1:

OrthCondition1 := int(sum(cos(2*k*Pi*x/a)*cos(2*m*Pi*x/a), k = 1 .. N), x = 0 .. a) = (1/2)*a

orthogonality codition 2:

OrthCondition2 := int(sum(cos(2*l*Pi*x/b)*cos(2*m*Pi*x/b), l = 1 .. N), x = 0 .. b) = (1/2)*b;