An asymptotic expansion of a ratio of products of gamma functions is derived. It generalizes a formula which was stated by Dingle, first proved by Paris, and recently reconsidered by Olver.
Liu, M. C. (1969). Some applications of asymptotic approximation [master's thesis, The University of Hong Kong]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0029-1812201200009898
BARTH, K. F., & BRANNAN, D. A. (1996). ASYMPTOTIC TRACTS OF HARMONIC FUNCTIONS III. International Journal of Mathematics and Mathematical Sciences, 1996(), 633-636. https://doi.org/10.1155/S0161171296000890