OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) p. 134.
FORMULA
-log(4)/4 - PolyGamma(1/2)/4 = EulerGamma/4
From Amiram Eldar, Jul 21 2020: (Start)
Equals -Integral_{x=0..oo} e^(-x^2)*x*log(x) dx.
Equals Integral_{x=0..oo} (e^(-x^4) - e^(-x^2))/x dx. (End)
EXAMPLE
0.1443039162253832151516280225206006077605398339849808997...
MATHEMATICA
RealDigits[EulerGamma/4, 10, 107] // First
PROG
(PARI) default(realprecision, 100); Euler/4 \\ G. C. Greubel, Aug 28 2018
(Magma) R:= RealField(100); EulerGamma(R)/4; // G. C. Greubel, Aug 28 2018
CROSSREFS
Cf. A001620 (gamma(1,1) = EulerGamma),
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),
KEYWORD
AUTHOR
Jean-François Alcover, Apr 11 2015
STATUS
approved