Properties and applications of the reciprocal logarithm numbers

DOI10.1007/s10440-008-9325-0zbMath1208.11032OpenAlexW2037419927WikidataQ60691962 ScholiaQ60691962MaRDI QIDQ966483

Victor Kowalenko

Publication date: 23 April 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-008-9325-0

zbMATH Keywords

power series expansionsharmonic numbersEuler's constantrecursion relationreciprocal logarithm numbers

Mathematics Subject Classification ID

Applications of graph theory (05C90) Bell and Stirling numbers (11B73) Combinatorial aspects of partitions of integers (05A17) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items

A note on some constants related to the zeta-function and their relationship with the Gregory coefficients, Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\), Generalized Cosecant Numbers and the Hurwitz Zeta Function, Applications of the cosecant and related numbers, On a finite sum involving inverse powers of cosines, Unnamed Item, A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations, Expansions of generalized Euler's constants into the series of polynomials in \(\pi^{- 2}\) and into the formal enveloping series with rational coefficients only, Factorization of Hermite subdivision operators from polynomial over-reproduction, Generalized cosecant numbers and trigonometric inverse power sums, Rebuttal of Kowalenko's paper as concerns the irrationality of Euler's constant \(\gamma\), Three notes on Ser's and Hasse's representations for the zeta-functions, Generalizing the reciprocal logarithm numbers by adapting the partition method for a power series expansion, Unnamed Item, Sequence transformations in proofs of irrationality of some fundamental constants, Limit distribution of the coefficients of polynomials with only unit roots, Unnamed Item

Uses Software

• Mathematica
• OEIS

Cites Work

• On Stirling numbers and Euler sums
• The non-relativistic charged Bose gas in a magnetic field. II: Quantum properties.
• Exactification of the asymptotics for Bessel and Hankel functions.
• The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation
• Asymptotics for the Kummer function of Bose plasmas
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