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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 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.
11J72 Irrationality; linear independence over a field
11Y60 Evaluation of number-theoretic 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) · JFM 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
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