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%I #15 Jan 07 2024 01:53:43
%S 0,8,4,3,1,9,6,8,8,4,3,3,1,6,2,9,5,5,9,3,9,0,4,0,3,5,6,8,0,3,7,5,4,8,
%T 0,0,1,2,8,1,2,4,3,7,3,8,2,5,9,1,7,0,6,8,5,2,3,0,3,0,3,9,9,9,3,8,7,7,
%U 8,8,1,6,6,3,2,4,9,5,4,3,5,1,9,7,6,3,9,7,8,7,3,1,6,0,2,9,5,3,3,2,0,1,0,1,2
%N Decimal expansion of the generalized Euler constant gamma(3,8).
%H G. C. Greubel, <a href="/A256782/b256782.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 EulerGamma/8 + 1/8*(Pi/2*(sqrt(2)-1) + log(2) - sqrt(2)*log(sqrt(2)+1)).
%F Equals -(psi(3/8) + log(8))/8 = -(A354633 + A016631)/8. - _Amiram Eldar_, Jan 07 2024
%e 0.08431968843316295593904035680375480012812437382591706852303...
%t Join[{0}, RealDigits[-3/8*Log[2] - PolyGamma[3/8]/8, 10, 104] // First]
%o (PARI) default(realprecision, 100); Euler/8 + 1/8*(Pi/2*(sqrt(2)-1) + log(2) - sqrt(2)*log(sqrt(2)+1)) \\ _G. C. Greubel_, Aug 28 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/8 + (1/8)*(Pi(R)/2*(Sqrt(2)-1) + Log(2) - Sqrt(2)*Log(Sqrt(2)+1)); // _G. C. Greubel_, Aug 28 2018
%Y Cf. A001620 (EulerGamma), A016631, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)), A354633.
%K nonn,cons,easy
%O 0,2
%A _Jean-François Alcover_, Apr 10 2015
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