The Best Bounds in Gautschi-Kershaw Inequalities

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Qi, Feng, Guo, Bai-Ni and Chen, Chao-Ping (2005) The Best Bounds in Gautschi-Kershaw Inequalities. Research report collection, 8 (2).


By employing the convolution theorem of Laplace transforms, some asymptotic formulas and integral representations of the gamma, psi and polygamma functions, and other analytic techniques, this note provides an alternative proof of a monotonicity and convexity property by N. Elezović, C. Giordano and J. Pečarić in [4] to establish the best bounds in Gautschi- Kershaw inequalities. Moreover, some (logarithmically) complete monotonicity results on functions related to Gautschi-Kershaw inequalities are remarked.

Item type Article
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords monotonicity, convexity, gamma function, psi function, polygamma function, Gautschi-Kershaw inequality, logarithmically completely monotonic function
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