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A256845
Decimal expansion of the generalized Euler constant gamma(2,4).
10
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, 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, 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
OFFSET
0,2
LINKS
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),
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).
Sequence in context: A188657 A021697 A276635 * A340193 A340196 A016707
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved