On the harmonic number expansion by Ramanujan

DOI10.1186/1029-242X-2013-222zbMath1331.11119WikidataQ59301484 ScholiaQ59301484MaRDI QIDQ2637569

Chao-Ping Chen, Cristinel Mortici

Publication date: 12 February 2014

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

zbMATH Keywords

asymptotic expansioninequalityharmonic numbersEuler-Mascheroni constantpsi functionpolygamma functions

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Gamma, beta and polygamma functions (33B15) Evaluation of number-theoretic constants (11Y60)

Related Items

A new sequence convergent to Euler-Mascheroni constant ⋮ On the coefficients of asymptotic expansion for the harmonic number by Ramanujan ⋮ The monotonicity and convexity of a function involving psi function with applications ⋮ On the Ramanujan harmonic number expansion ⋮ Harmonic number expansions of the Ramanujan type ⋮ Riordan array approach to the coefficients of Ramanujan's harmonic number expansion ⋮ On new sequences converging towards the Ioachimescu's constant ⋮ On the Ramanujan-Lodge harmonic number expansion ⋮ Optimizing the coefficients of the Ramanujan expansion ⋮ Multiple-correction and continued fraction approximation ⋮ Ramanujan's harmonic number expansion and two identities for Bernoulli numbers ⋮ Multiple-correction and faster approximation ⋮ Asymptotic series related to Ramanujan's expansion for the harmonic number ⋮ Continued fraction inequalities for the Euler-Mascheroni constant ⋮ Some sharp continued fraction inequalities for the Euler-Mascheroni constant

Cites Work

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• On some inequalities for the gamma and psi functions