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%I #14 Jan 07 2024 01:54:57
%S 7,1,0,2,8,9,7,9,3,0,6,4,0,9,3,6,9,7,3,1,3,7,6,6,4,7,5,7,9,5,0,8,2,6,
%T 1,0,3,0,4,0,6,1,0,4,2,4,9,6,9,3,2,9,4,0,8,5,3,4,7,9,8,8,5,1,3,3,0,4,
%U 2,3,8,7,9,7,2,6,1,5,9,7,1,4,6,4,2,0,6,9,5,0,7,3,9,8,0,5,9,9,2,7,6,1,9
%N Decimal expansion of the generalized Euler constant gamma(1,4).
%H G. C. Greubel, <a href="/A256778/b256778.txt">Table of n, a(n) for n = 0..10000</a>
%H D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa27/aa27121.pdf">Euler constants for arithmetic progressions</a>, Acta Arith. 27 (1975), p. 134.
%F Equals (2*EulerGamma + Pi + 2*log(2))/8.
%F Equals Sum_{n>=0} (1/(4n+1) - 1/2*arctanh(2/(4n+3))).
%F Equals -(psi(1/4) + log(4))/4 = (A020777 - A016627)/4. - _Amiram Eldar_, Jan 07 2024
%e 0.71028979306409369731376647579508261030406104249693294...
%t RealDigits[EulerGamma/4 + Pi/8 + Log[2]/4, 10, 103] // First
%o (PARI) default(realprecision, 100); (2*Euler + Pi + 2*log(2))/8 \\ _G. C. Greubel_, Aug 27 2018
%o (Magma) R:=RealField(100); (2*EulerGamma(R) + Pi(R) + 2*Log(2))/8; // _G. C. Greubel_, Aug 27 2018
%Y Cf. A001620 (EulerGamma), A016627, A020777, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256779-A256784 (selection of ruler-and-compass constructible gamma(r,k)).
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Apr 10 2015
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