The exact evaluation of the corner-to-corner resistance of anM×Nresistor network: asymptotic expansion

We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s = 1, our result is R(N x N) = 4/pi logN + 0.077318 + 0.266070/N(2) - 0.534779/N(4) + O(1/N(6)).