Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d, II: Special kinematics

Abstract: Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\ Lett.\ B {\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The calculations are considered all external kinematic configurations and internal mass assignments. Analytic formulas are expressed in terms of generalized hypergeometric series such as Gauss $_2F_1$, Appell $F_1$ and Lauricella $F_S$ functions.