On the degree of the weighted geometric mean as a complete Bernstein function

DOI10.1007/s13370-014-0279-2zbMath1329.26054OpenAlexW2027191563MaRDI QIDQ897993

Bai-Ni Guo, Feng Qi

Publication date: 8 December 2015

Published in: Afrika Matematika (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13370-014-0279-2

zbMATH Keywords

operator monotone functiongeometric meancompletely monotonic functioncomplete Bernstein functioncompletely monotonic degree

Mathematics Subject Classification ID

Means (26E60) Monotonic functions, generalizations (26A48)

Related Items (15)

Some properties of the Schröder numbers ⋮ Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Unnamed Item ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ The harmonic and geometric means are Bernstein functions ⋮ The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function ⋮ Lévy-Khintchine representation of Toader-Qi mean ⋮ A Solution to fourth Qi's Conjecture on a complete monotonicity ⋮ The reciprocal of the weighted geometric mean is a Stieltjes function ⋮ Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers ⋮ Integral representations and complete monotonicity of remainders of the binet and Stirling formulas for the gamma function ⋮ The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform ⋮ Integral representations of the large and little Schröder numbers ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions

Cites Work

• Unnamed Item
• Unnamed Item
• A completely monotonic function involving the tri-gamma function and with degree one
• An integral representation for the weighted geometric mean and its applications
• Integral representations and properties of Stirling numbers of the first kind
• Lévy-Khintchine representations of the weighted geometric mean and the logarithmic mean
• Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
• On complete monotonicity of some functions related to means
• Lévy-Khintchine representation of the geometric mean of many positive numbers and applications
• Complete monotonicity of the logarithmic mean
• Bernstein functions. Theory and applications

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