A256845 - OEIS

%I #18 Sep 08 2022 08:46:12

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

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

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

%N Decimal expansion of the generalized Euler constant gamma(2,4).

%H G. C. Greubel, <a href="/A256845/b256845.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(1/2)/4 = EulerGamma/4

%F From _Amiram Eldar_, Jul 21 2020: (Start)

%F Equals -Integral_{x=0..oo} e^(-x^2)*x*log(x) dx.

%F Equals Integral_{x=0..oo} (e^(-x^4) - e^(-x^2))/x dx. (End)

%e 0.1443039162253832151516280225206006077605398339849808997...

%t RealDigits[EulerGamma/4, 10, 107] // First

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

%o (Magma) R:= RealField(100); EulerGamma(R)/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