Absolutely monotonic functions related to Euler's gamma function and Barnes' double and triple gamma function

DOI10.1007/s00605-010-0197-9zbMath1241.33004OpenAlexW2029649663MaRDI QIDQ538399

Stamatis Koumandos, Henrik Laurberg Pedersen

Publication date: 25 May 2011

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-010-0197-9

zbMATH Keywords

asymptotic expansiondouble gamma functionabsolute monotonicitytriple gamma function

Mathematics Subject Classification ID

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

Related Items

Completely monotonic degree of a function involving trigamma and tetragamma functions ⋮ Multiple Gamma Functions and Their Applications ⋮ More asymptotic expansions for the Barnes \(G\)-function ⋮ Some two-sided inequalities for multiple Gamma functions and related results ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Completely monotonic degrees for a difference between the logarithmic and psi functions ⋮ Qi's conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and trigamma functions ⋮ Bounds for completely monotonic degrees of remainders in asymptotic expansions of the digamma function

Cites Work

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• Remarks on some completely monotonic functions
• 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
• On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function
• On the asymptotic expansion of the logarithm of Barnes triple gamma function
• On some inequalities for the gamma and psi functions
• On Barnes' multiple zeta and gamma functions