Wendel's and Gautschi's inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions
نویسندگان
چکیده
In the article, presented are sufficient and necessary conditions for a class of functions involving the ratio of two gamma functions to be logarithmically completely monotonic. From this, some inequalities for bounding the ratio of two gamma functions are refined, extended and sharpened readily, and double inequalities on the divided differences of the psi and polygamma functions are derived straightforwardly.
منابع مشابه
Bounds for the Ratio of Two Gamma Functions-from Wendel's and Related Inequalities to Logarithmically Completely Monotonic Functions
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...
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ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 205 شماره
صفحات -
تاریخ انتشار 2008