General one-loop generating function by integration-by-part relations

Abstract

In this paper, we have studied the general generating function of reduction for one-loop integrals with arbitrary tensor structure in the numerator and arbitrary power distribution of propagators in the denominator. Using integration-by-part relations, we have established the partial differential equations for these generating functions and solved them analytically with compact form. These results provide useful information for the analytical structure of reduction coefficients and guidance for applying the generating function method to reductions of higher loop integrals. Published by the American Physical Society 2025