The Best Bounds in Gautschi-Kershaw Inequalities

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. Elezovic, C. Giordano and J. Pecaric 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.

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