A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums

Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48)

Related Items (14)

Complete monotonicity of divided differences of the di- and tri-gamma functions with applications ⋮ Wendel's and Gautschi's inequalities: refinements, extensions, and a class of logarithmically completely monotonic functions ⋮ Complete monotonicity of some functions involving polygamma functions ⋮ Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic ⋮ A class of logarithmically completely monotonic functions associated with a gamma function ⋮ Logarithmically complete monotonicity properties relating to the gamma function ⋮ Bounds for the ratio of two gamma functions -- from Wendel's and related inequalities to logarithmically completely monotonic functions ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ 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 ⋮ A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw's inequality ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Sharp Inequalities for Polygamma Functions ⋮ COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

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