Asymptotic expansion for \(\log n!\) in terms of the reciprocal of a triangular number

DOI10.1007/s10474-010-0027-5zbMath1240.11042OpenAlexW2006288072MaRDI QIDQ626034

Gergő Nemes

Publication date: 25 February 2011

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-010-0027-5

zbMATH Keywords

asymptotic expansionapproximationBernoulli numbersStirling's formulaGamma functionfactorialRamanujan's formula

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Gamma, beta and polygamma functions (33B15) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Numerical approximation and evaluation of special functions (33F05) Saturation in approximation theory (41A40)

Related Items (23)

On the coefficients of asymptotic expansion for the harmonic number by Ramanujan ⋮ Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\) ⋮ On the Ramanujan harmonic number expansion ⋮ Harmonic number expansions of the Ramanujan type ⋮ Stirling expansions into negative powers of a triangular number ⋮ 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 ⋮ An explicit formula for the coefficients in Laplace's method ⋮ Ramanujan's formula for the harmonic number ⋮ Sharp inequalities and asymptotic expansions for the gamma function ⋮ Optimizing the coefficients of the Ramanujan expansion ⋮ Inequalities and asymptotic expansions for the gamma function related to Mortici's formula ⋮ Approximations for the higher order coefficients in an asymptotic expansion for the gamma function ⋮ 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 ⋮ Asymptotic expansions for the reciprocal of the gamma function ⋮ Inequalities and asymptotic expansions for the gamma function ⋮ Asymptotic series related to Ramanujan's expansion for the harmonic number ⋮ An asymptotic series related to Ramanujan's expansion for the \(n\)th harmonic number ⋮ Asymptotic expansions for the gamma function ⋮ Ramanujan's asymptotic expansion for the harmonic numbers

Cites Work

• Inequalities for the gamma function relating to asymptotic expansions
• Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number
• ON RAMANUJAN'S DOUBLE INEQUALITY FOR THE GAMMA FUNCTION
• On the asymptotic representation of the Euler gamma function by Ramanujan
• Unnamed Item

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