Inequalities associated with Barnes \(G\)-function

DOI10.1016/J.EXMATH.2010.07.001zbMath1216.33004OpenAlexW2037184352MaRDI QIDQ533112

Chao-Ping Chen

Publication date: 2 May 2011

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2010.07.001

zbMATH Keywords

gamma functionRiemann zeta functioninequalitypsi functionpolygamma functionsBarnes \(G\)-function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48)

Related Items (11)

Bounds for triple gamma functions and their ratios ⋮ Multiple Gamma Functions and Their Applications ⋮ Asymptotic expansions for Barnes \(G\)-function ⋮ Asymptotic expansions and complete monotonicity properties for the Barnes \(G\)-function ⋮ Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants ⋮ Asymptotic formulas for the triple gamma function \(\varGamma _{3}\) by means of its integral representation ⋮ Inequalities involving the multiple psi function ⋮ More asymptotic expansions for the Barnes \(G\)-function ⋮ Asymptotic expansions for certain mathematical constants and special functions ⋮ Some two-sided inequalities for multiple Gamma functions and related results ⋮ Some new properties of the Barnes G-function and related results

Cites Work

• Some mathematical constants
• The remainder in Ruijsenaars' asymptotic expansion of Barnes double gamma function
• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
• Spectral functions, special functions and the Selberg zeta function
• Extremals of determinants of Laplacians
• Zeta regularized products and functional determinants on spheres
• On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function
• On the remainder in an asymptotic expansion of the double gamma function
• Inequalities for the double gamma function
• Determinants of Laplacians and Multiple Gamma Functions
• The determinant of the Laplacian on the n-sphere
• On Barnes' multiple zeta and gamma functions
• An asymptotic expansion of the double gamma function
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