On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas

DOI10.1016/j.amc.2015.12.004zbMath1410.33005OpenAlexW2238484273MaRDI QIDQ671042

Chao-Ping Chen

Publication date: 20 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.12.004

zbMATH Keywords

gamma functionasymptotic expansioninequality

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities for sums, series and integrals (26D15)

Related Items

A double inequality related with Burnside's formula

Cites Work

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• Asymptotic expansions of the gamma function related to Windschitl's formula
• On Stirling's formula remainder
• Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula
• New upper bounds of \(n!\)
• Unified treatment of several asymptotic formulas for the gamma function
• A generated approximation of the gamma function related to Windschitl's formula
• A new asymptotic expansion and some inequalities for the gamma function
• On Ramanujan's large argument formula for the gamma function
• Some inequalities and monotonicity properties associated with the gamma and psi functions
• A refinement of Ramanujan's factorial approximation
• Ramanujan's estimate for the gamma function via monotonicity arguments
• Ramanujan formula for the generalized Stirling approximation
• The asymptotic series of the generalized Stirling formula
• A new Stirling series as continued fraction
• Asymptotic expansions of the generalized Stirling approximations
• Asymptotic expansion for \(\log n!\) in terms of the reciprocal of a triangular number
• Improved asymptotic formulas for the gamma function
• New improvements of the Stirling formula
• Remarks on asymptotic expansions for the gamma function
• A general asymptotic formula of the gamma function based on the Burnside's formula
• A new fast asymptotic series for the gamma function
• Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function
• A class of integral approximations for the factorial function
• New asymptotic expansion for the gamma function
• An ultimate extremely accurate formula for approximation of the factorial function
• Completely monotonic and related functions
• Inequalities and asymptotic expansions associated with the Ramanujan and nemes formulas for the gamma function
• A continued fraction approximation of the gamma function
• Inequalities and asymptotic expansions for the gamma function
• A generated approximation related to Gosper's formula and Ramanujan's formula
• Best estimates of the generalized Stirling formula
• Sharp inequalities related to Gosper's formula
• The special functions and their approximations. Vol. I, II
• A generated approximation related to Burnside's formula
• Product Approximations via Asymptotic Integration
• On Gospers formula for the Gamma function
• Asymptotic formulae associated with the Wallis power function and digamma function
• Very accurate approximations for the factorial function
• Very accurate estimates of the polygamma functions
• Decision procedure for indefinite hypergeometric summation
• ON RAMANUJAN'S DOUBLE INEQUALITY FOR THE GAMMA FUNCTION
• More accurate approximations for the Gamma function
• Complete monotonicity properties and asymptotic expansions of the logarithm of the gamma function
• Asymptotic formulas for the gamma function by Gosper
• Ramanujan's Lost Notebook
• On the asymptotic representation of the Euler gamma function by Ramanujan

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