A new Stirling series as continued fraction
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Publication:621779
DOI10.1007/s11075-010-9370-4zbMath1213.33007OpenAlexW1989999673MaRDI QIDQ621779
Publication date: 28 January 2011
Published in: Numerical Algorithms (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11075-010-9370-4
Bell and Stirling numbers (11B73) Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Convergence and divergence of continued fractions (40A15)
Related Items (58)
A series of sequences convergent to Euler's constant ⋮ Windschitl type approximation formulas for the gamma function ⋮ Some new improved classes of convergence towards Euler's constant ⋮ Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula ⋮ Some best approximation formulas and inequalities for the Wallis ratio ⋮ Some new exponential-function estimates of the Somos' quadratic recurrence constant ⋮ Some new sequences and inequalities related to Euler's constant ⋮ New sequences with continued fraction towards Euler's constant ⋮ A quicker continued fraction approximation of the gamma function related to the Windschitl's formula ⋮ A new general asymptotic formula and inequalities involving the volume of the unit ball ⋮ A new quicker sequence convergent to Euler's constant ⋮ A generated approximation related to Burnside's formula ⋮ Some quicker classes of sequences convergent to Euler's constant ⋮ Some quicker approximations and inequalities of the Wallis ratio by continued fraction ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Unified treatment of several asymptotic formulas for the gamma function ⋮ New continued fraction expansions and inequalities for \(n!\) into negative powers of a triangular number ⋮ Some asymptotic formulas and inequalities about gamma and psi functions based on continued fractions ⋮ Improved convergence towards Glaisher-Kinkelin's and Bendersky-Adamchik's constants ⋮ Two families of approximations for the gamma function ⋮ A kind of new continued fraction approximation of gamma function based on Mortici's formula ⋮ A generated approximation of the gamma function related to Windschitl's formula ⋮ A new asymptotic expansion and some inequalities for the gamma function ⋮ Some new quicker approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants ⋮ A new fast asymptotic series 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 ⋮ Optimizing the coefficients of the Ramanujan expansion ⋮ A continued fraction approximation of the gamma function ⋮ Some new quicker continued fraction approximations for the gamma function related to the Nemes' formula ⋮ Some inequalities and monotonicity properties associated with the gamma and psi functions ⋮ Approximation formulas for Landau's constants ⋮ Some new continued fraction approximation of Euler's constant ⋮ A quicker approximation of the gamma function towards the Windschitl's formula by continued fraction ⋮ Monotonicity properties, inequalities and asymptotic expansions associated with the gamma function ⋮ Two asymptotic expansions for gamma function developed by Windschitl's formula ⋮ On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas ⋮ New quicker sequences and inequalities with continued fraction towards Euler's constant ⋮ New asymptotic formulas and inequalities for the gamma function based on continued fractions ⋮ Some new convergent sequences of Glaisher-Kinkelin's and Bendersky-Adamchik's constants ⋮ Some quicker continued fraction approximations and inequalities towards Euler's constant ⋮ A new approximation of the gamma function by expanding the Windschitl's formula ⋮ Continued fractions and inequalities about \(\left( 1+\frac{1}{x}\right)^x\) ⋮ Continued fraction approximations and inequalities for the gamma function by Burnside ⋮ Padé approximant related to asymptotics for the gamma function ⋮ Some new convergent sequences and inequalities of Euler's constant ⋮ Inequalities and asymptotic expansions for the gamma function ⋮ A new sharp approximation for the gamma function related to Burnside's formula ⋮ A generated approximation related to Gosper's formula and Ramanujan's formula ⋮ Continued fraction estimates for the psi function ⋮ On some convergence to the constant \(e\) and proof of Keller's limit ⋮ Some new approximations of Glaisher-Kinkelin's and Bendersky-Adamchik's constants by continued fraction ⋮ Asymptotic expansions for the gamma function ⋮ A general asymptotic formula of the gamma function based on the Burnside's formula ⋮ Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function ⋮ A continued product approximation for the gamma function ⋮ A product approximation of the gamma function ⋮ Necessary and sufficient conditions for functions involving the psi function to be completely monotonic
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