COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

DOI10.1017/S0004972712001025zbMath1280.26018MaRDI QIDQ2865135

Pietro Cerone, Feng Qi, Sever Silvestru Dragomir

Publication date: 28 November 2013

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

inequalitynecessary and sufficient conditiondivided differencepsi functionpolygamma functioncomplete monotonicityratio of two gamma functionslogarithmically complete monotonicity

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Monotonic functions, generalizations (26A48)

Related Items

Logarithmically completely monotonic functions related to the \(q\)-gamma function and its applications ⋮ Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ Bounds for Bateman's \(G\)-function and its applications ⋮ Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ Some inequalities for the trigamma function in terms of the digamma function ⋮ Complete monotonicity of functions involving the \(q\)-trigamma and \(q\)-tetragamma functions ⋮ Bounds for the ratio of two gamma functions: from Wendel's asymptotic relation to Elezović-Giordano-Pečarić's theorem ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions

Cites Work

• Complete monotonicity of functions involving the \(q\)-trigamma and \(q\)-tetragamma functions
• Bounds for the ratio of two gamma functions
• Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
• Logarithmically completely monotonic functions relating to the gamma function
• Integral representation of some functions related to the gamma function
• On infinitely divisible matrices, kernels, and functions
• The best bounds in Gautschi's inequality
• Three classes of logarithmically completely monotonic functions involving gamma and psi functions
• A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums
• What is the Laplace Transform?