Generating Functions in Two Dimensional Quantum Gravity

Abstract

We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and double torus. Our method is also applicable to more higher genus. Each generating function can be expressed by a ``specific heat'' function for sphere. Universal terms, which are survived in the double scaling limit can be easily picked out from our exact solutions. We also find that the regular part of the spherical generating function is at most bilinear in coupling constants of source terms.