Best estimates of the generalized Stirling formula
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Publication:2266985
DOI10.1016/J.AMC.2009.12.013zbMath1186.33003OpenAlexW1980155288MaRDI QIDQ2266985
Publication date: 26 February 2010
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2009.12.013
Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities for sums, series and integrals (26D15)
Related Items (33)
The best rational remainders in the Stirling formula ⋮ A more accurate approximation for the gamma function ⋮ Complete characterizations of the gamma function ⋮ On Stirling's formula remainder ⋮ The gamma function via interpolation ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Unified treatment of several asymptotic formulas for the gamma function ⋮ The proof of Muqattash-Yahdi conjecture ⋮ Ramanujan formula for the generalized Stirling approximation ⋮ The asymptotic series of the generalized Stirling formula ⋮ New approximation formulas for evaluating the ratio of gamma functions ⋮ Estimating the digamma and trigamma functions by completely monotonicity arguments ⋮ A new Stirling series as continued fraction ⋮ A new fast asymptotic series for the gamma function ⋮ On some Euler-Mascheroni type sequences ⋮ On Ramanujan's large argument formula for the gamma function ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ Some properties of functions related to the gamma, psi and tetragamma functions ⋮ Inequalities and asymptotic expansions for the gamma function related to Mortici's formula ⋮ Improved asymptotic formulas for the gamma function ⋮ Monotonicity properties of the volume of the unit ball in \({\mathbb{R}^{n}}\) ⋮ Approximation formulas for Landau's constants ⋮ 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 ⋮ Multiple-correction and faster approximation ⋮ Ramanujan's estimate for the gamma function via monotonicity arguments ⋮ Continued fraction estimates for the psi function ⋮ A class of integral approximations for the factorial function ⋮ New improvements of the Stirling formula ⋮ Asymptotic expansions for the gamma function ⋮ New inequalities for gamma and digamma functions
Cites Work
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- Series involving the zeta function and multiple Gamma functions
- Improved convergence towards generalized Euler-Mascheroni constant
- Some mathematical constants
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- Integrals involving a function associated with the Euler-Maclaurin summation formula
- Multiple gamma and related functions
- Product Approximations via Asymptotic Integration
- OPTIMIZING THE RATE OF CONVERGENCE IN SOME NEW CLASSES OF SEQUENCES CONVERGENT TO EULER'S CONSTANT
- Decision procedure for indefinite hypergeometric summation
- Some new considerations on the Bernoulli numbers, the factorial function, and Riemann's zeta function.
- Improving Stirling's formula
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