On the Ramanujan-Lodge harmonic number expansion
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Publication:903020
DOI10.1016/j.amc.2014.11.088zbMath1328.41008OpenAlexW1990325120MaRDI QIDQ903020
Mark B. Villarino, Cristinel Mortici
Publication date: 4 January 2016
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2014.11.088
Bernoulli and Euler numbers and polynomials (11B68) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)
Related Items (12)
On the Ramanujan harmonic number expansion ⋮ Harmonic number expansions of the Ramanujan type ⋮ Investigations about the Euler-Mascheroni constant and harmonic numbers ⋮ New continued fraction expansions and inequalities for \(n!\) into negative powers of a triangular number ⋮ Riordan array approach to the coefficients of Ramanujan's harmonic number expansion ⋮ On new sequences converging towards the Ioachimescu's constant ⋮ Asymptotic expansions and continued fraction approximations for harmonic numbers ⋮ Ramanujan's formula for the harmonic number ⋮ Optimizing the coefficients of the Ramanujan expansion ⋮ Ramanujan's harmonic number expansion and two identities for Bernoulli numbers ⋮ Asymptotic series related to Ramanujan's expansion for the harmonic number ⋮ On some convergence to the constant \(e\) and proof of Keller's limit
Cites Work
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- Ramanujan formula for the generalized Stirling approximation
- New improvements of the Stirling formula
- New approximations of the gamma function in terms of the digamma function
- A continued fraction approximation of the gamma function
- On the harmonic number expansion by Ramanujan
- Product Approximations via Asymptotic Integration
- A Quicker Convergence to Euler's Constant
- Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number
- 75.9 Euler’s Constant
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