×

Rebuttal of Kowalenko’s paper as concerns the irrationality of Euler’s constant \(\gamma\). (English) Zbl 1263.11068

The irrationality of Euler’s constant \(\gamma\) is widely believed to be true, but it still remains a major open problem in number theory to give a proof. In this short note, the authors rebut two claims of V. Kowalenko [Acta Appl. Math. 109, No. 2, 413–437 (2010; Zbl 1208.11032)], namely, that he proved the irrationality of \(\gamma\), and that his rational series for \(\gamma\) is new.

MSC:

11J72 Irrationality; linear independence over a field
11Y60 Evaluation of number-theoretic constants

Citations:

Zbl 1208.11032
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Gourdon, X., Sebah, P.: Collection of formulae for the Euler constant. http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.pdf
[2] Kluyver, J.C.: De constante van Euler en de natuurlijke getallen. Amst. Ak. Versl. 33, 149–151 (1924)
[3] Kluyver, J.C.: Euler’s constant and natural numbers. Proc. K. Ned. Akad. Wet. 27, 142–144 (1924). http://www.dwc.knaw.nl/DL/publications/PU00015025.pdf
[4] Kowalenko, V.: Properties and applications of the reciprocal logarithm numbers. Acta Appl. Math. 109, 413–437 (2010) · Zbl 1208.11032 · doi:10.1007/s10440-008-9325-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.