The system of partial differential equations for the $C_{{}_0}$ function

Abstract

We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{{}_0}$ function. The approach can be employed to evaluate the coefficient of arbitrary power of $\epsilon$ in the expansion of a scalar integral, where $D=4-2\epsilon$ denotes the time-space dimension.

Comments: Latex, 68 pages