Almost analytic solutions to equilibrium sequences of irrotational binary polytropic stars for n=1

A solution to an equilibrium of irrotational binary polytropic stars in Newtonian gravity is expanded in a power of epsilon = a(0)/R, where R and a(0) are the separation of the binary system and the radius of each star for R = infinity. For the polytropic index n = 1, the solutions are given almost analytically up to order epsilon(6). We have found that in general an equilibrium solution should have the velocity component along the orbital axis and that the central density should decrease when R decreases. Our almost analytic solutions can be used to check the validity of numerical solutions.