A new asymptotic expansion and some inequalities for the gamma function
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Publication:401996
DOI10.1016/J.JNT.2014.01.025zbMath1296.33006OpenAlexW2080688721MaRDI QIDQ401996
Publication date: 27 August 2014
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jnt.2014.01.025
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 (21)
A more accurate approximation for the gamma function ⋮ 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 ⋮ Some new approximations and inequalities of the sequence \((1+1/n)^n\) and improvements of Carleman's inequality ⋮ Asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ New continued fraction expansions and inequalities for \(n!\) into negative powers of a triangular number ⋮ Bounds for the gamma function ⋮ A kind of new continued fraction approximation of gamma function based on Mortici's formula ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function ⋮ A double inequality related with Burnside's formula ⋮ 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 ⋮ On some convergence to the constant \(e\) and proof of Keller's limit ⋮ Asymptotic expansions for the gamma function ⋮ A general asymptotic formula of the gamma function based on the Burnside's formula ⋮ On Burnside type approximation for the gamma function ⋮ New inequalities for gamma and digamma functions ⋮ Some new continued fraction estimates of the Somos' quadratic recurrence constant
Cites Work
- Ramanujan formula for the generalized Stirling approximation
- A new Stirling series as continued fraction
- New improvements of the Stirling formula
- On new sequences converging towards the Euler-Mascheroni constant
- New asymptotic expansion for the gamma function
- A continued fraction approximation of the gamma function
- Product Approximations via Asymptotic Integration
- Very accurate estimates of the polygamma functions
- Decision procedure for indefinite hypergeometric summation
- On some inequalities for the gamma and psi functions
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