Double integration of functions involving bessel functions and cosines/sines

[moonkhan]

Can we integrate double integrals involving bessel functions and sinusoids in maple. Also, the overlap of sine and cosine over the range of 0 to 2 * Pi must be exactly zero, but, in maple, it gives some value (of the order of -129). Is there any software, which can compute the exact double integral.
The function i am trying to integrate numerically (please correct me if i am doing rigth by solving numerically):

"((((besselj(const1,const2)./besselk(const1,const2)).*besselk(const1,const1*r/const3).*cos(const*(phi))).*conj((besselj(const2,(kpaa2/a).*(r)).*cos(const2*(phi))))).*r)"
with 0<=phi>=2*Pi, and 0<=r>=125e-6.

I tried with matlab's builtin functions, but the same problem of accuracy.

Thanks in advance.
Moon

 

[fresh_42]

You cannot expect that you have a zero error margin with a calculation in a computer. $-129$ is already pretty low and you will have to write your own program if you want to do better. In the end it always will be a compromise, since a computer is a discrete machine and you want to use it for calculations with real, i.e. infinitely long numbers.