New improvements of the Stirling formula
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Publication:711306
DOI10.1016/j.amc.2010.06.007zbMath1202.33004OpenAlexW2091374796MaRDI QIDQ711306
Publication date: 25 October 2010
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2010.06.007
gamma functionrate of convergenceasymptotic expansionStirling's formulafactorial functionnumeric series
Gamma, beta and polygamma functions (33B15) Computation of special functions and constants, construction of tables (65D20) Numerical approximation and evaluation of special functions (33F05) Approximations and expansions (41A99)
Related Items (43)
Estimates for Wallis' ratio and related functions ⋮ Complete characterizations of the gamma function ⋮ Asymptotic expansions of the gamma function related to Windschitl's formula ⋮ Completely monotonic functions and inequalities associated to some ratio of gamma function ⋮ On Stirling's formula remainder ⋮ Estimates of the function and quotient by Minc-Sathre ⋮ Some best approximation formulas and inequalities for the Wallis ratio ⋮ Multiple Gamma Functions and Their Applications ⋮ Asymptotic formulas for sequence factorial of arithmetic progression ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Continued fraction approximation for the gamma function based on the tri-gamma function ⋮ Unified treatment of several asymptotic formulas for the gamma function ⋮ Improved approximation formulas and inequalities for the Wallis ratio ⋮ A generated approximation of the gamma function related to Windschitl's formula ⋮ A new asymptotic expansion and some inequalities for the gamma function ⋮ Approximation for the gamma function via the tri-gamma function ⋮ A new fast asymptotic series for the gamma function ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function ⋮ On the Ramanujan-Lodge harmonic number expansion ⋮ Asymptotic formulas for the triple gamma function \(\varGamma _{3}\) by means of its integral representation ⋮ Some inequalities associated to the ratio of Pochhammer k-symbol ⋮ Inequalities and asymptotic expansions for the gamma function related to Mortici's formula ⋮ Removing magic from the normal distribution and the Stirling and Wallis formulas ⋮ Some inequalities for the trigamma function in terms of the digamma function ⋮ Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function ⋮ Completely monotonic functions and inequalities associated to some ratios of the Pochhammer \(k\)-symbol ⋮ On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas ⋮ Continued fraction approximation and inequality of the gamma function ⋮ Continued fraction approximation for the gamma function by the tri-gamma function ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Inequalities and asymptotic expansions for the gamma function ⋮ Asymptotic formulas associated with psi function with applications ⋮ Sharp approximation formulas and inequalities for the Wallis ratio by continued fraction ⋮ A method to construct continued-fraction approximations and its applications ⋮ Inequalities and asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Improved asymptotic formula and inequalities for the ratio of Pochhammer \(k\)-symbol ⋮ Asymptotic expansions for the gamma function ⋮ New improved inequalities associated with ratios of gamma functions ⋮ On Burnside type approximation for the gamma function ⋮ Asymptotic approximations for non-integer order derivatives of monomials ⋮ New inequalities for gamma and digamma functions ⋮ Some sharp continued fraction inequalities for the Euler-Mascheroni constant
Uses Software
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