Unified approaches to the approximations of the gamma function

DOI10.1016/j.jnt.2015.12.016zbMath1342.33005OpenAlexW2292591088MaRDI QIDQ5964557

Weiping Wang

Publication date: 29 February 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.12.016

zbMATH Keywords

gamma functionapproximationsBell polynomials

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (9)

The gamma function via interpolation ⋮ Harmonic number expansions of the Ramanujan type ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ Gamma and Factorial in the Monthly ⋮ Some asymptotic expansions on hyperfactorial functions and generalized Glaisher-Kinkelin constants ⋮ New Fourier transform containing a pair of complex Euler Γ-functions with a monomial: Mathematical and physical applications ⋮ New asymptotic expansions on hyperfactorial functions ⋮ Asymptotic expansions related to hyperfactorial function and Glaisher-Kinkelin constant ⋮ Improvements of asymptotic approximation formulas for the factorial function

Cites Work

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• Asymptotic expansions of the gamma function related to Windschitl's formula
• Some new asymptotic approximations of the gamma function based on Nemes' formula, Ramanujan's formula and Burnside's formula
• Unified treatment of several asymptotic formulas for the gamma function
• Two families of approximations for the gamma function
• On Ramanujan's large argument formula for the gamma function
• Approximations for the higher order coefficients in an asymptotic expansion for the gamma function
• A refinement of Ramanujan's factorial approximation
• A substantial improvement of the Stirling formula
• Ramanujan formula for the generalized Stirling approximation
• The asymptotic series of the generalized Stirling formula
• Improved asymptotic formulas for the gamma function
• Efficient computation of Ihara coefficients using the Bell polynomial recursion
• 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
• Inequalities for the gamma function
• Remarks on Stirling's formula and on approximations for the double factorial.
• An ultimate extremely accurate formula for approximation of the factorial 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
• Sharp inequalities related to Gosper's formula
• A generated approximation related to Burnside's formula
• Very accurate approximations for the factorial function
• More accurate approximations for the Gamma function
• On the asymptotic representation of the Euler gamma function by Ramanujan

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