Some new convergent sequences and inequalities of Euler's constant

DOI10.1016/J.JMAA.2014.05.018zbMath1300.40002OpenAlexW1964328076MaRDI QIDQ2252486

Dawei Lu

Publication date: 17 July 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.05.018

zbMATH Keywords

Euler's constant

Mathematics Subject Classification ID

Approximation to limiting values (summation of series, etc.) (40A25)

Related Items (14)

A new sequence convergent to Euler-Mascheroni constant ⋮ The monotonicity and convexity of a function involving psi function with applications ⋮ Monotonicity rules for the ratio of two Laplace transforms with applications ⋮ Some new sequences and inequalities related to Euler's constant ⋮ New sequences with continued fraction towards Euler's constant ⋮ Some new approximations and inequalities of the sequence \((1+1/n)^n\) and improvements of Carleman's inequality ⋮ New quicker sequences and inequalities with continued fraction towards Euler's constant ⋮ Some quicker continued fraction approximations and inequalities towards Euler's constant ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ On some convergence to the constant \(e\) and proof of Keller's limit ⋮ Inequalities and asymptotic expansions for the psi function and the Euler-Mascheroni constant ⋮ A logarithmic estimate for harmonic sums and the digamma function, with an application to the Dirichlet divisor problem ⋮ Continued fraction inequalities for the Euler-Mascheroni constant ⋮ Necessary and sufficient conditions for functions involving the psi function to be completely monotonic

Cites Work

• A new Stirling series as continued fraction
• On new sequences converging towards the Euler-Mascheroni constant
• A continued fraction approximation of the gamma function
• A new quicker sequence convergent to Euler's constant
• Product Approximations via Asymptotic Integration
• A Quicker Convergence to Euler's Constant
• OPTIMIZING THE RATE OF CONVERGENCE IN SOME NEW CLASSES OF SEQUENCES CONVERGENT TO EULER'S CONSTANT
• Very accurate estimates of the polygamma functions
• 75.9 Euler’s Constant
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