A256782 Decimal expansion of the generalized Euler constant gamma(3,8).

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

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

Equals EulerGamma/8 + 1/8*(Pi/2*(sqrt(2)-1) + log(2) - sqrt(2)*log(sqrt(2)+1)).

Equals -(psi(3/8) + log(8))/8 = -(A354633 + A016631)/8. - Amiram Eldar, Jan 07 2024

Example

0.08431968843316295593904035680375480012812437382591706852303...

Mathematica

Join[{0}, RealDigits[-3/8*Log[2] - PolyGamma[3/8]/8, 10, 104] // First]

Prog

(PARI) default(realprecision, 100); Euler/8 + 1/8*(Pi/2*(sqrt(2)-1) + log(2) - sqrt(2)*log(sqrt(2)+1)) \\ G. C. Greubel, Aug 28 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/8 + (1/8)*(Pi(R)/2*(Sqrt(2)-1) + Log(2) - Sqrt(2)*Log(Sqrt(2)+1)); // G. C. Greubel, Aug 28 2018

Crossrefs

Cf. A001620 (EulerGamma), A016631, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)), A354633.

Sequence in context: A337170 A050135 A109595 * A071832 A327121 A091475

Adjacent sequences: A256779 A256780 A256781 * A256783 A256784 A256785

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 10 2015

Status

approved