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New Vacca-type rational series for Euler’s constant \(\gamma\) and its “alternating” analog \(\ln\,\frac4\pi\). (English) Zbl 1258.11103
Chudnovsky, David (ed.) et al., Additive number theory. Festschrift in honor of the sixtieth birthday of Melvyn B. Nathanson. New York, NY: Springer (ISBN 978-0-387-37029-3/hbk; 978-0-387-68361-4/ebook). 331-340 (2010).
The author use the binary expansion of an integer to derive linear, quadratic, and cubic analogs foe Vacca’s rational series for gamma. Open problems on further extensions of the results are discussed, and a history of the formulas is given.
For the entire collection see [Zbl 1196.11005].

MSC:
11Y60 Evaluation of number-theoretic constants
65B10 Numerical summation of series
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