A256781 Decimal expansion of the generalized Euler constant gamma(1,8).

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

Offset

0,1

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 Sum_{n>=0} (1/(8n+1) - 1/4*arctanh(4/(8n+5))).

Equals -(psi(1/8) + log(8))/8 = -(A250129 + A016631)/8. - Amiram Eldar, Jan 07 2024

Example

0.788631390202002367443880819838976661978118204921...

Mathematica

RealDigits[-3/8*Log[2] - PolyGamma[1/8]/8, 10, 105] // First

Prog

(PARI) Euler/8 + 1/8*(Pi/2*(sqrt(2)+1) + log(2) + sqrt(2)*log(sqrt(2) + 1)) \\ Michel Marcus, Apr 10 2015
(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)), A250129, A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

Sequence in context: A338815 A197810 A085361 * A248224 A092290 A156571

Adjacent sequences: A256778 A256779 A256780 * A256782 A256783 A256784

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 10 2015

Status

approved