Asymptotic expansions for Barnes \(G\)-function

DOI10.1016/j.jnt.2013.08.007zbMath1373.33003OpenAlexW1982254624MaRDI QIDQ2406705

Chao-Ping Chen

Publication date: 5 October 2017

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.08.007

zbMATH Keywords

gamma functionasymptotic expansionBernoulli numbersBarnes \(G\)-function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (15)

Computing the Barnes \(G\)-function and the gamma function in the entire complex plane ⋮ Scaling limits for non-intersecting polymers and Whittaker measures ⋮ Some asymptotic expansions on hyperfactorial functions and generalized Glaisher-Kinkelin constants ⋮ New asymptotic expansions and Padé approximants related to the triple gamma function ⋮ Asymptotic expansions of the Glaisher-Kinkelin and Choi-Srivastava constants ⋮ 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 ⋮ New asymptotic expansions on hyperfactorial functions ⋮ Asymptotic expansions related to hyperfactorial function and Glaisher-Kinkelin constant ⋮ Unified treatment of several asymptotic expansions concerning some mathematical constants ⋮ More asymptotic expansions for the Barnes \(G\)-function ⋮ Asymptotic expansions for certain mathematical constants and special functions ⋮ Asymptotic expansions related to the Glaisher-Kinkelin constant and its analogues ⋮ New approximations for the higher order coefficients in an asymptotic expansion for the Barnes \(G\)-function ⋮ Some new properties of the Barnes G-function and related results

Cites Work

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• Inequalities associated with Barnes \(G\)-function
• 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
• Approximating the constants of Glaisher-Kinkelin type
• Asymptotic expansions related to Glaisher-Kinkelin constant based on the Bell polynomials
• 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
• Some inequalities and monotonicity properties associated with the gamma and psi functions and the BarnesG-function
• Glaisher–Kinkelin constant
• 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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