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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.
##### MSC:
 11J72 Irrationality; linear independence over a field 11Y60 Evaluation of number-theoretic constants
##### Keywords:
Euler’s constant; irrationality; Kluyver’s numbers; rebuttal
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##### 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) · 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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