New properties of the divided difference of psi and polygamma functions

DOI10.1007/s13398-021-01084-6zbMath1483.33002OpenAlexW3173962748MaRDI QIDQ2050217

Zhen-Hang Yang, Jing-Feng Tian

Publication date: 30 August 2021

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-021-01084-6

zbMATH Keywords

monotonicityconvexitysharp boundspsi functionpolygamma functions

Mathematics Subject Classification ID

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 (2)

Complete monotonicity involving the divided difference of polygamma functions ⋮ Decreasing properties of two ratios defined by three and four polygamma functions

Cites Work

• Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function
• An inequality involving the gamma and digamma functions
• Complete monotonicity of divided differences of the di- and tri-gamma functions with applications
• Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications
• Monotonicity of a mean related to polygamma functions with an application
• A completely monotonic function involving the tri-gamma function and with degree one
• Integral representations and complete monotonicity of remainders of the binet and Stirling formulas for the gamma function
• Some monotonicity properties of gamma and \(q\)-gamma functions
• Sharp bounds for psi function
• Complete monotonicity of some functions involving polygamma functions
• On some properties of digamma and polygamma functions
• Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
• Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic
• Monotonicity rules for the ratio of two Laplace transforms with applications
• Monotonicity and inequalities for the gamma function
• A double inequality for the trigamma function and its applications
• A comparison theorem for two divided differences and applications to special functions
• Inequalities for the gamma and polygamma functions
• Fisher-Rao geometry of Dirichlet distributions
• Some properties of the divided difference of psi and polygamma functions
• A ratio of finitely many gamma functions and its properties with applications
• On complete monotonicity for several classes of functions related to ratios of gamma functions
• Some completely monotonic functions involving the polygamma functions
• A positive answer to Bhatia-Li conjecture on the monotonicity for a new mean in its parameter
• Asymptotic expansions of Gurland's ratio and sharp bounds for their remainders
• Some properties of several functions involving polygamma functions and originating from the sectional curvature of the beta manifold
• Quantization and clustering on Riemannian manifolds with an application to air traffic analysis
• New bounds for the function involving incomplete gamma function
• Asymptotic expansions for the gamma function in terms of hyperbolic functions
• Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function
• Complete monotonicity involving some ratios of gamma functions
• A CLASS OF COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE PSI AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS
• An alternative proof of Elezović-Giordano-Pečarić's theorem
• Inequalities for the gamma function relating to asymptotic expansions
• Very accurate estimates of the polygamma functions
• Some properties of the psi and polygamma functions
• Inequalities for the Polygamma Functions
• Sharp inequalities for the digamma and polygamma functions
• The best bounds in Gautschi's inequality
• A class of completely mixed monotonic functions involving the gamma function with applications
• Refinements of lower bounds for polygamma functions
• A new asymptotic expansion of a ratio of two gamma functions and complete monotonicity for its remainder
• Complete monotonicity and inequalites involving Gurland's ratios of gamma functions
• Sharp Inequalities for Polygamma Functions
• Sub- and superadditive properties of Euler's gamma function
• SOME COMPLETELY MONOTONIC FUNCTIONS INVOLVING THE GAMMA AND POLYGAMMA FUNCTIONS
• On some inequalities for the gamma and psi functions
• Subadditive functions
• Mean-value inequalities for the polygamma functions
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