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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 {\it 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.
11Y60Evaluation of constants
Full Text: DOI arXiv
[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) · Zbl 50.0159.02
[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