Generating functions in two-dimensional quantum gravity Original Research Article

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 a double torus. Our method is also applicable to higher genus. Each generating function can be expressed by a “specific heat” function for the sphere. Universal terms, which 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 the coupling constants of the source terms.