A256778 Decimal expansion of the generalized Euler constant gamma(1,4).

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

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 (2*EulerGamma + Pi + 2*log(2))/8.

Equals Sum_{n>=0} (1/(4n+1) - 1/2*arctanh(2/(4n+3))).

Equals -(psi(1/4) + log(4))/4 = (A020777 - A016627)/4. - Amiram Eldar, Jan 07 2024

Example

0.71028979306409369731376647579508261030406104249693294...

Mathematica

RealDigits[EulerGamma/4 + Pi/8 + Log[2]/4, 10, 103] // First

Prog

(PARI) default(realprecision, 100); (2*Euler + Pi + 2*log(2))/8 \\ G. C. Greubel, Aug 27 2018
(Magma) R:=RealField(100); (2*EulerGamma(R) + Pi(R) + 2*Log(2))/8; // G. C. Greubel, Aug 27 2018

Crossrefs

Cf. A001620 (EulerGamma), A016627, A020777, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256779-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

Sequence in context: A229819 A194655 A197037 * A218620 A195911 A231096

Adjacent sequences: A256775 A256776 A256777 * A256779 A256780 A256781

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 10 2015

Status

approved