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A CLASS OF COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE PSI AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS
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 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;
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 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
1.
COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE TRI- AND TETRA-GAMMA FUNCTIONS,;

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Bounds for the ratio of two gamma functions: from Wendel’s asymptotic relation to Elezović-Giordano-Pečarić’s theorem, Journal of Inequalities and Applications, 2013, 2013, 1, 542  crossref(new windwow)
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