The reciprocal of the weighted geometric mean is a Stieltjes function

DOI10.1007/s40590-016-0151-5zbMath1390.30048OpenAlexW2522445797MaRDI QIDQ1743777

Feng Qi, Bai-Ni Guo

Publication date: 16 April 2018

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-016-0151-5

zbMATH Keywords

Cauchy integral formulaintegral representation, weighted geometric mean of two positive numbers

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items (7)

Integral representations of bivariate complex geometric mean and their applications ⋮ On complete monotonicity of linear combination of finite psi functions ⋮ Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function ⋮ Alternative proofs of some formulas for two tridiagonal determinants ⋮ Integral representations of the large and little Schröder numbers ⋮ Refining and reversing the weighted arithmetic-geometric mean inequality involving convex functionals and application for the functional entropy

Cites Work

• The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform
• On the degree of the weighted geometric mean as a complete Bernstein function
• Sums of series of Rogers dilogarithm functions
• The harmonic and geometric means are Bernstein functions
• A complete monotonicity property of the gamma function
• An integral representation for the weighted geometric mean and its applications
• Lévy-Khintchine representations of the weighted geometric mean and the logarithmic mean
• Integral representation of some functions related to the gamma function
• On complete monotonicity of some functions related to means
• Lévy-Khintchine representation of the geometric mean of many positive numbers and applications
• A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function
• Some properties of functions related to the gamma and psi functions
• Bernstein functions. Theory and applications
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