I. K. Kazarinoff [Edinburgh Math. Notes, 40 (1956), pp. 19–21] and G. N. Watson [Proc. Edinburgh Math. Soc., 2, 11 (1959), pp. 7–9] gave extensions and proofs of gamma function inequalities closely associated with Wallis’ product. One of Watson’s proofs generated considerable interest, particularly among statisticians. Here some of. the extensive previous background is outlined and further results are developed.
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Jacques Dutka (1985) studied this question.