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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 thispaper. The calculations are considered all external kinematic configurationsand internal mass assignments. Analytic formulas are expressed in terms ofgeneralized hypergeometric series such as Gauss $_2F_1$, Appell $F_1$ andLauricella $F_S$ functions.

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