Ch. 7 presents the theory behind an alternative method of regularising a divergent
series known as Mellin-Barnes (MB) regularisation. As a result, the regularised values for more
general versions of the two types of terminants presented earlier are derived in terms of MB inte-grals, which are often more expedient to evaluate than the regularised values obtained via Borel
summation. Furthermore, unlike the Borel-summed forms for the regularised values, the MB-regularised forms are not affected by Stokes lines and sectors, but are instead valid over domains
of convergence, which extend further than Stokes sectors and overlap one another. Thus, there
are two different MB-regularised forms for obtaining the regularised value in the common regions
of overlapping domains of convergence, which include the Stokes lines of Borel summation. To
demonstrate that MB regularisation need not only be applied to an asymptotic series, a numeri-cal example determining the regularised value of an abbreviated version of the binomial theorem
is also presented for two different values of the index ρand for various values of the variablez
outside the unit disk of absolute convergence.
