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A256848 Decimal expansion of the generalized Euler constant gamma(3,5) (negated).

%I A256848 #13 Sep 08 2022 08:46:12
%S A256848 0,1,3,7,6,3,7,3,9,7,0,8,1,8,1,9,9,1,9,6,8,0,1,9,0,7,6,8,8,3,9,9,1,1,
%T A256848 3,9,6,0,3,0,1,3,4,1,9,9,1,5,7,8,2,1,0,2,7,2,9,1,9,2,5,2,5,6,4,2,6,0,
%U A256848 2,0,2,9,2,9,3,3,1,1,0,5,9,7,1,1,3,5,8,2,8,2,0,7,4,6,8,0,1,5,8,1,3,9,8,7,7,9,9,8,6
%N A256848 Decimal expansion of the generalized Euler constant gamma(3,5) (negated).
%H A256848 G. C. Greubel, <a href="/A256848/b256848.txt">Table of n, a(n) for n = 0..10000</a>
%H A256848 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 A256848 Equals -log(5)/5 - PolyGamma(3/5)/5.
%F A256848 Equals EulerGamma/5 + Pi/(10*sqrt(2*(5+sqrt(5)))) - Pi/(2*sqrt(10*(5+sqrt(5)))) + log(5)/20 + log((5-sqrt(5))/(5+sqrt(5)))/(4*sqrt(5)).
%e A256848 -0.013763739708181991968019076883991139603013419915782102729...
%t A256848 Join[{0}, RealDigits[-Log[5]/5 - PolyGamma[3/5]/5, 10, 108] // First  ]
%o A256848 (PARI) default(realprecision, 100); Euler/5 + Pi/(10*sqrt(2*(5+sqrt(5)))) - Pi/(2*sqrt(10*(5+sqrt(5)))) + log(5)/20 + log((5-sqrt(5))/(5+sqrt(5)))/(4*sqrt(5)) \\ _G. C. Greubel_, Aug 28 2018
%o A256848 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/5 + Pi(R)/(10*Sqrt(2*(5+Sqrt(5)))) - Pi(R)/(2*Sqrt(10*(5+Sqrt(5)))) + Log(5)/20 + Log((5-Sqrt(5))/(5+Sqrt(5)))/(4*Sqrt(5)); // _G. C. Greubel_, Aug 28 2018
%Y A256848 Cf. A001620 (gamma(1,1) = EulerGamma),
%Y A256848 Primitive ruler-and-compass constructible gamma(r,k): A228725 (1,2), A256425 (1,3), A256778 (1,4), A256779 (1,5), A256780 (2,5), A256781 (1,8), A256782 (3,8), A256783 (1,12), A256784 (5,12),
%Y A256848 Other gamma(r,k) (1 <= r <= k <= 5): A239097 (2,2),  A256843 (2,3),  A256844 (3,3), A256845 (2,4), A256846 (3,4), A256847 (4,4), A256848 (3,5), A256849 (4,5), A256850 (5,5).
%K A256848 nonn,cons,easy
%O A256848 0,3
%A A256848 _Jean-François Alcover_, Apr 11 2015