Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants

DOI10.2298/aadm220414024hzbMath1524.41081OpenAlexW4294591162MaRDI QIDQ6169408

Chao-Ping Chen, Xue-Feng Han, Hari M. Srivastava

Publication date: 11 July 2023

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/aadm220414024h

zbMATH Keywords

Riemann zeta functionasymptotic expansionEuler-Maclaurin summation formulaStirling's formulaGlaisher-Kinkelin constantChoi-Srivastava constantsBarnes \(G\)-functiongeneralized Glaisher-Kinkelin constantWallis' sequence

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Convergence and divergence of series and sequences (40A05) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Cites Work

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• Completely monotonic functions and inequalities associated to some ratio of gamma function
• Further refinements of Gurland's formula for \({\pi}\)
• Asymptotic expansions of the Glaisher-Kinkelin and Choi-Srivastava constants
• An asymptotic approximation of Wallis' sequence
• Asymptotic formulas for the triple gamma function \(\varGamma _{3}\) by means of its integral representation
• Completely monotone functions and the Wallis ratio
• Inequalities associated with Barnes \(G\)-function
• New approximation formulas for evaluating the ratio of gamma functions
• Sharp inequalities and complete monotonicity for the Wallis ratio
• Series involving the zeta function and multiple Gamma functions
• 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
• Certain classes of series involving the zeta function
• Polygamma functions of negative order
• Certain classes of series associated with the zeta function and multiple gamma functions
• Birth, growth and computation of pi to ten trillion digits
• Unified treatment of several asymptotic expansions concerning some mathematical constants
• On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas
• Zeta regularized products and functional determinants on spheres
• Sur la fonction gamma généralisée
• A set of mathematical constants arising naturally in the theory of the multiple Gamma functions
• Inequalities and asymptotic expansions associated with the Wallis sequence
• Sharp inequalities and asymptotic expansion associated with the Wallis sequence
• Asymptotic expansions for Barnes \(G\)-function
• 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
• Inequalities and asymptotic expansions of the Wallis sequence and the sum of the Wallis ratio
• A new method for establishing and proving accurate bounds for the Wallis ratio
• Some inequalities and monotonicity properties associated with the gamma and psi functions and the BarnesG-function
• A Probabilistic Proof of Wallis's Formula for π
• Asymptotic formulae associated with the Wallis power function and digamma function
• Glaisher–Kinkelin constant
• Wallis-Ramanujan-Schur-Feynman
• Determinants of Laplacians and Multiple Gamma Functions
• The determinant of the Laplacian on the n-sphere
• Some new properties of the Barnes G-function and related results
• Asymptotic expansions for certain mathematical constants and special functions
• Asymptotic expansions of the multiple quotients of gamma functions with applications
• An Elementary Proof of the Wallis Product Formula for pi
• On Barnes' multiple zeta and gamma functions
• An asymptotic expansion of the double gamma function

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