a general theory for handling all divergent series, a quest that has stretched over centuries, but to this day remains elusive. One important reason why such a theory remains elusive is that the divergence can be different for diverse problems requiring different approaches or methods to regularize them. In fact, we shall see that the asymptotic forms derived in this work are composed of an infinite power series that can be regularized via generalized terminants and another infinite series, which is logarithmically divergent and thus, needs to be handled differently.

Discovered in the 1730’s [@wiki12] Stirling’s approximation/formula is a famous result for obtaining values of the factorial function or its more general version, the gamma function, denoted by $\Gamma(z)$. Because the gamma function exhibits rapid exponential growth, those working in asymptotics frequently study the alternative version of the approximation, where it is expressed in terms of its logarithm, i.e. $\ln \Gamma(z)$. From an asymptotics point of view, $\ln \Gamma(z)$ is a far more formidable function than $\Gamma(z)$, because it possesses the multivaluedness of the logarithm function. To compensate for taking the logarithm, it is often assumed that one has at their disposal an exponentiating routine that will render values of 