I have an engineering background and I am faced with the following problem.
Green's function for the discrete Laplacian on a square lattice is well known and I think it is a discrete harmonic function. Is there a formula for its conjugate harmonic function?
If I'm not mistaken, the continuous analogs of these functions would be the real and imaginary part of $\log(z) = \ln(r)+i\theta$.
Thank you for any help you can provide!