\Gamma(z)$ to generate the complete asymptotic expansion for $\ln \Gamma(z)$, in which the asymptotic series is now expressed as an infinite sum of generalized terminants. Moreover, a general theory for deriving regularized values of the remainders for both types of these series via Borel summation is elucidated in Ref. [@kow09]. With the aid of this theory, new asymptotic forms for $\ln \Gamma(z)$ are presented and proved for all Stokes sectors and lines. Because of an infinite number of singularities situated on each Stokes line, on each occasion when crossing from one Stokes sector to its neighbouring sector an extra infinite series appears in the asymptotic forms, which is referred to as the Stokes discontinuity term. Since these series can become logarithmically divergent, they must be regularized according to Lemma 2.2, which describes the regularization of the standard Taylor series expansion of $\ln(1+z)$. The section concludes with how the expression for $\ln \Gamma(z)$ can be used to derive new results for the digamma function and Euler’s constant.

Because such symbols as $\sim$, $\simeq$, $\pm \cdot$, $\geq$, $\leq$ and the Landau gauge symbols of $O()$ and $o()$ abound in the discipline, as stated in the foreword to Ref. [@kow09], one can virtually 