Bounds for the Ratio of Two Gamma Functions-from Wendel's and Related Inequalities to Logarithmically Completely Monotonic Functions
نویسنده
چکیده
In the survey paper, along one of several main lines of bounding the ratio of two gamma functions, the authors retrospect and analyse Wendel’s double inequality, Kazarinoff’s refinement of Wallis’ formula, Watson’s monotonicity, Gautschi’s double inequality, Kershaw’s first double inequality, and the (logarithmically) complete monotonicity results of functions involving ratios of two gamma or q-gamma functions obtained by Bustoz, Ismail, Lorch, Muldoon, and other mathemat cians. 1. Preliminaries In this paper, we need some definitions, notions, and notations below. 1.1. The gamma and q-gamma functions. It is well known that the classical Euler’s gamma function may be defined for Rez > 0 by
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