Hi all!

F is a delta function:

F:=delta(x-x[0])*delta(y-y[0])

I want it be expaned through trigonometric series:

F:=sum(sum(Q[k*l]*sin(l*Pi*x/a)*sin(k*Pi*y/b), k = 1 .. infinity), l = 1 .. infinity)

So I want to get every Q:

Q[k, l] := `assuming`([4*(int(int(f[z1]*sin(l*Pi*x/a)*sin(k*Pi*y/b), x = 0 .. b), y = 0 .. a))/(a*b)], [k::posint, l::posint, a > 0, b > 0])

But it result in (when x[0]:=a/2, y[0]:=b/2):

4*(int(int(F[0]*exp(I*omega*t)*delta(x-x[0])*delta(y-y[0])*sin(l*Pi*x/a)*sin(k*Pi*y/b), x = 0 .. b), y = 0 .. a))/(a*b)

I wonder HOW CAN I GET THE EXACT RESULT:Q[k, l] := 4*sin(l*Pi/a)*sin(k*Pi/b)/(a*b)

THANKS!

Hi all

kx,ky is the wavenumber, how can I get the 4 cases of piecewise function according to kx=0,kx≠0 and ky=0,ky≠0. Thanks

J := `assuming`([4*(int(int(JJ*exp(-I*(kx*x+ky*y))*sin(2*l*pi*x/a)*sin(2*k*pi*y/b), x = 0 .. a, AllSolutions), y = 0 .. b, AllSolutions))/(a*b)], [k::posint, l::posint, a > 0, b > 0, JJ > 0])

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;