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

Author

Jean-François Alcover, Apr 11 2015

Keywords

• nonn
• cons
• easy

Examples

			0.1443039162253832151516280225206006077605398339849808997...
		

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.

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).

Programs

Magma

R:= RealField(100); EulerGamma(R)/4; // G. C. Greubel, Aug 28 2018

Mathematica

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

PARI

default(realprecision, 100); Euler/4 \\ G. C. Greubel, Aug 28 2018

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)