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
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Bühring, W. (2000). An asymptotic expansion for a ratio of products of gamma functions. International Journal of Mathematics and Mathematical Sciences, 24(8), 505–510. https://doi.org/10.1155/s0161171200010310