The asymptotic series of the generalized Stirling formula

DOI10.1016/j.camwa.2010.05.025zbMath1201.33002OpenAlexW1988360472MaRDI QIDQ611366

Cristinel Mortici

Publication date: 14 December 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.05.025

zbMATH Keywords

gamma functionapproximationsasymptotic seriesStirling formulaBurnside formulacompletely monotonicity

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Numerical approximation and evaluation of special functions (33F05)

Related Items (16)

A more accurate approximation for the gamma function ⋮ Complete characterizations of the gamma function ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Unified treatment of several asymptotic formulas for the gamma function ⋮ Two families of approximations for the gamma function ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ A curious identity arising from Stirling's formula and saddle-point method on two different contours ⋮ Inequalities and asymptotic expansions for the gamma function related to Mortici's formula ⋮ Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function ⋮ On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Inequalities and asymptotic expansions for the gamma function ⋮ Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions ⋮ Unified approaches to the approximations of the gamma function ⋮ Asymptotic expansions for the gamma function ⋮ A note on complete monotonicity of the remainder in Stirling's formula

Cites Work

• Sharp inequalities and complete monotonicity for the Wallis ratio
• Improved convergence towards generalized Euler-Mascheroni constant
• A class of integral approximations for the factorial function
• A remark on a class of double inequalities of Batir
• An inequality for ratios of gamma functions
• An ultimate extremely accurate formula for approximation of the factorial function
• New approximations of the gamma function in terms of the digamma function
• Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\)
• Best estimates of the generalized Stirling formula
• Sharp inequalities related to Gosper's formula
• Product Approximations via Asymptotic Integration
• Very accurate estimates of the polygamma functions
• On some inequalities for the gamma and psi functions
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