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

J W Essam, F Y Wu
2008 Journal of Physics A: Mathematical and Theoretical  
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_NxN = (4/pi) log N + 0.077318 + 0.266070/N^2 - 0.534779/N^4 + O(1/N^6).
doi:10.1088/1751-8113/42/2/025205 fatcat:apxtdrxc4bgldd5tajuhb5zdsi