A CLASS OF COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE PSI AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 48, Issue 3, 2011, pp.655-667
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2011.48.3.655

Title & Authors

A CLASS OF COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE PSI AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS

Guo, Bai-Ni; Qi, Feng;

Guo, Bai-Ni; Qi, Feng;

Abstract

A class of functions involving divided differences of the psi and tri-gamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving the ratio of two gamma functions and originating from the establishment of the best upper and lower bounds in Kershaw's double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in and respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized.

Keywords

completely monotonic function;divided difference;gamma function;psi function;tri-gamma function;probability integral;error function;double factorial;ratio;volume of unit ball;monotonicity;convexity;inequality;generalization;application;

Language

English

Cited by

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