New approximation formulas for evaluating the ratio of gamma functions

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A deterministic and computable Bernstein-von Mises theorem (2019, background): “In order to approximate these moments in the limit p →∞ while k remains fixed, we can consider the following approximation of the ratio of the Gamma function (see Mortici [2010] and additional references therein): for all s ∈ [0, 1] n1−s ≤ Γ (n+ 1) Γ (n+ s) ≤ (n+ 1) (275)”
Bounds for the Ratio of Two Gamma Functions (2009, methodology): “Finally, we would like to recommend the articles [25, 26, 27, 28, 30, 37, 40, 43, 44, 45, 46, 47, 48, 49, 50, 54, 59, 60, 68, 73, 74, 75, 77, 81, 82, 108, 109, 111, 116] and closely related references therein to the readers for finding new developments and applications of the gamma function, polygam”
PhaseMax: Convex Phase Retrieval via Basis Pursuit (2016, unknown): “We have used the fact that √ (n/2 − 1)/π 1 n−1 > 1 √8n for n ≥ 4, and also the “Wallis ratio” bound (n/2) ((n−1)/2) ≥ √ n/2 − 1 [57], [58].”