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A239097 Decimal expansion of -(gamma-log(2))/2.

%I A239097 #18 Sep 08 2022 08:46:07
%S A239097 0,5,7,9,6,5,7,5,7,8,2,9,2,0,6,2,2,4,4,0,5,3,6,0,0,1,5,6,8,7,8,8,7,0,
%T A239097 6,8,5,1,6,6,7,0,3,9,9,2,1,0,1,6,5,8,2,7,6,5,7,4,5,6,3,8,7,3,0,4,2,6,
%U A239097 2,9,4,7,5,9,6,0,1,5,0,2,2,3,3,4,4,5,8,1,3,1,8,5,2,3,3,5,9,6,9,0,1,3,6,8,5,0,1,6,8,8,5,3,8,1,8,0,1,6,2,6,3,6,2,5,0,8,1,1,0,6,3,5,7,9
%N A239097 Decimal expansion of -(gamma-log(2))/2.
%C A239097 Decimal expansion of the generalized Euler constant -gamma(0,2).
%H A239097 G. C. Greubel, <a href="/A239097/b239097.txt">Table of n, a(n) for n = 0..10000</a>
%H A239097 D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa27/aa27121.pdf">Euler constants for arithmetical progressions</a>, Collection of articles in memory of Juriĭ Vladimirovič Linnik. Acta Arith. 27 (1975), 125--142. MR0369233 (51 #5468). See p. 128.
%F A239097 From _Amiram Eldar_, Jun 30 2020: (Start)
%F A239097 Equals Sum_{k>=1} zeta(2*k+1)/((2*k+1)*2^(2*k+1)).
%F A239097 Equals Sum_{k>=1} arctanh(1/(2*k)) - 1/(2*k). (End)
%e A239097 .057965757829206224405360015687887068516670399210165827657456...
%t A239097 Join[{0}, RealDigits[(Log[2] - EulerGamma)/2, 10, 100][[1]]] (* _G. C. Greubel_, Aug 28 2018 *)
%o A239097 (PARI) (log(2)-Euler)/2 \\ _Charles R Greathouse IV_, Mar 25 2014
%o A239097 (Magma) SetDefaultRealField(RealField(100)); R:= RealField();
%o A239097 (Log(2) - EulerGamma(R))/2; // _G. C. Greubel_, Aug 28 2018
%Y A239097 Cf. A001620, A228725.
%K A239097 nonn,cons
%O A239097 0,2
%A A239097 _N. J. A. Sloane_, Mar 23 2014