An explicit expression of generating function for one-loop tensor reduction

Abstract

Abstract This work introduces an explicit expression for the generating function for the reduction of an n-gon to an (n – k)-gon. A novel recursive relation of generating function is formulated based on Feynman Parametrization in projective space, involving a single ordinary differential equation. The explicit formulation of generating functions provides crucial insights into the complex analytic structure inherent in loop amplitudes.