On a square grid of 1 ohm resistors, the effective resistance between the node at (0,0) and the node at (p,q) is given by the following expression. R[p,q] = (1/(4 pi^2)) int (F(x,y), x=-pi..pi, y=-pi..pi), F(x,y) = [1 - cos(p x + q y)] / [2 - (cos x + cos y)]. Maple 11 can do these. I will say that Maple 11 is a winner, while Maple 9 is a loser. Here are some low-order results. The pi's are always in the denominator. R[1,0] 1/2 R[1,1] 2/pi R[2,0] 2 - 4/pi R[2,1] 4/pi - 1/2 R[2,2] 8/3pi R[3,0] 17/2 - 24/pi R[3,1] 46/3pi - 4 R[3,2] 1/2 + 4/3pi R[3,3] 46/15pi R[4,0] 40-368/3pi R[4,1] 80/pi - 49/2 R[4,2] 6 - 236/15pi R[4,3] 24/5pi - 1/2 R[4,4] 352/105pi R[5,5] 1126/315pi R[6,6] 13016/3465pi R[7,7] 176138/45045pi The denominators in the diagonal terms, R[p,p] seem to fit the pattern 1*3*5*...*(2p -1). Gene ____________________________________________________________________________________ Looking for last minute shopping deals? Find them fast with Yahoo! Search. http://tools.search.yahoo.com/newsearch/category.php?category=shopping