A256846 - OEIS

%I #13 Sep 08 2022 08:46:12

%S 0,7,5,1,0,8,3,7,0,3,3,3,3,5,4,6,1,2,3,0,1,8,9,4,3,7,0,0,2,4,7,9,3,1,

%T 1,0,7,4,5,2,3,1,3,0,7,3,4,6,8,4,3,5,1,4,3,9,0,2,5,6,2,6,2,9,4,3,9,1,

%U 1,7,1,3,5,9,8,9,3,6,2,7,8,1,9,2,8,0,1,7,5,5,5,9,5,7,2,3,2,7,4,2,3,3,6,1,0

%N Decimal expansion of the generalized Euler constant gamma(3,4) (negated).

%H G. C. Greubel, <a href="/A256846/b256846.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 -log(4)/4 - PolyGamma(3/4)/4 = EulerGamma/4 - Pi/8 - log(4)/4 + log(8)/4

%e -0.07510837033335461230189437002479311074523130734684351439...

%t Join[{0}, RealDigits[-Log[4]/4 - PolyGamma[3/4]/4, 10, 104] // First ]

%o (PARI) default(realprecision, 100); Euler/4 - Pi/8 - log(4)/4 + log(8)/4 \\ _G. C. Greubel_, Aug 28 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/4 - Pi(R)/8 - Log(4)/4 + Log(8)/4; // _G. C. Greubel_, Aug 28 2018

%Y Cf. A001620 (gamma(1,1) = EulerGamma),

%Y 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 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 nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Apr 11 2015