  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 $\varepsilon$ in the expansion of a scalar
integral, where $D=4-2\varepsilon$ denotes the time-space dimension.
