2
$\begingroup$

I was doing a physics problem and came across this integral which i need to solve

$$I(x,y,z)=\int_0^{2\pi}\int_0^{2\pi}\int_0^{2\pi}\left(\frac{1}{8\pi^3}\right)\left(\frac{1-\cos(nx+my+pz))}{3-\cos(x)-\cos(y)-\cos(z)}\right)dx\,dy\,dz$$

What i want to know is that does this integral evaluate to any specific function $f(n,m,p)$, and if so then how to calculate it?

I tried Wolframalpha's triple integral calculator but that doesn't seem to work..

Are there any other online applications i can use to calculate such integrals?

$\endgroup$
  • $\begingroup$ Are $n$ and $m$ and $p$ integers? $\endgroup$ – Greg.Paul May 21 '18 at 4:32
  • $\begingroup$ Where did you get this integral? Where does it come from? The symmetry is nice and can maybe be exploited. $\endgroup$ – Greg.Paul May 21 '18 at 4:33
  • $\begingroup$ @Greg.Paul Yes.They are actually coordinates of a node in a 3D grid and thus can have all possible integer values I saw this integral as a solution to a problem about calculating the equivalent resistance between nodes of an infinte N dimensional grid of unit resistors This is the case for N=3 or an infinite 3D grid of resistors Here is the link to the answer physics.stackexchange.com/questions/2072/… $\endgroup$ – Rutwik May 21 '18 at 4:34
  • $\begingroup$ iopscience.iop.org/article/10.1088/0022-3719/8/11/002 $\endgroup$ – Count Iblis May 21 '18 at 4:36
  • $\begingroup$ @CountIblis I cant open the PDF link.Requires some sort of a login $\endgroup$ – Rutwik May 21 '18 at 4:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.