In the context of Stirling’s formula for gamma functions and bounds for ratios of gamma functions, this work has a threefold purpose: (1) Outline recently published literature; (2) Synthesize techniques and results from Bhattacharjee and Mukhopadhyay (Commun Stat, Theory & Methods 39:1046–1053, 2010) and Mukhopadhyay (Commun Stat, Theory & Methods 40:1283–1297, 2011) which have gone perhaps unnoticed by some recent researchers; and (3) Incorporate new results for beta functions and useful bounds for the percentiles of a Studentized sample mean obtained from a normal distribution. This synthesized review may help in gaining a wider perspective about this area.