A256845 Decimal expansion of the generalized Euler constant gamma(2,4).

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

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),

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

Adjacent sequences: A256842 A256843 A256844 * A256846 A256847 A256848

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 11 2015

Status

approved