CLOSED EXPRESSIONS FOR SPECIFIC MASSIVE MULTILOOP SELF-ENERGY INTEGRALS

In this paper the class of N loop massive scalar self-energy diagrams with N + 1 propagators is studied in an arbitrary number of dimensions . As it is known these integrals cannot be expressed in terms of polyl ogarithms. Here it is shown, however, that they can be described by ge neralized hypergeometric functions of several variables, namely Larice lla functions. These results represent previous small and large moment um expansions in closed form. Numerical comparisons for the finite par t in four dimensions with a two-dimensional integral representation sh ow good agreement.