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J. Korean Math. Soc. 2008; 45(1): 273-287

Printed January 1, 2008

Copyright © The Korean Mathematical Society.

Some completely monotonic functions involving the gamma and polygamma functions

Ai-Jun Li and Chao-Ping Chen

Shanghai University, Henan Polytechnic University

Abstract

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In this paper, some logarithmically completely monotonic, strongly completely monotonic and completely monotonic functions related to the gamma, digamma and polygamma functions are established. Several inequalities, whose bounds are best possible, are obtained.

Keywords: logarithmically completely monotonic, completely monotonic, strongly completely monotonic, Laplace transforms

MSC numbers: 33B15, 26A48, 26A51

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