A new sharp approximation for the gamma function related to Burnside's formula

DOI10.1007/S11139-013-9534-7zbMath1306.33006OpenAlexW2023397224MaRDI QIDQ2254853

Dawei Lu

Publication date: 6 February 2015

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-013-9534-7

zbMATH Keywords

continued fractionStirling's formulaBurnside's formula

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Approximation by polynomials (41A10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (15)

A more accurate approximation for the gamma function ⋮ An accurate approximation formula for gamma function ⋮ Windschitl type approximation formulas for the gamma function ⋮ Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function ⋮ Completely monotonic functions and inequalities associated to some ratio of gamma function ⋮ A new continued fraction approximation and inequalities for the gamma function via the tri-gamma function ⋮ A family of Windschitl type approximations for gamma function ⋮ Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function ⋮ Monotonicity and inequalities for the gamma function ⋮ Two asymptotic expansions for gamma function developed by Windschitl's formula ⋮ Asymptotic formulas for gamma function with applications ⋮ Sharp Smith's bounds for the gamma function ⋮ Continued fraction approximations and inequalities for the gamma function by Burnside ⋮ On Burnside type approximation for the gamma function ⋮ Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function

Cites Work

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• A new Stirling series as continued fraction
• New asymptotic expansion for the gamma function
• A continued fraction approximation of the gamma function
• Product Approximations via Asymptotic Integration
• Decision procedure for indefinite hypergeometric summation
• On some inequalities for the gamma and psi functions

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