A256779 Decimal expansion of the generalized Euler constant gamma(1,5).

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

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/5 + Pi/10*sqrt(1 + 2/sqrt(5)) + log(5)/20 + sqrt(5)/10*log((1 + sqrt(5))/2).

Equals Sum_{n>=0} (1/(5n+1) - 2/5*arctanh(5/(10n+7))).

Equals -(psi(1/5) + log(5))/5 = (A200135 - A016628)/5. - Amiram Eldar, Jan 07 2024

Example

0.735920396831617584189289725844752893059997383987625...

Mathematica

RealDigits[-Log[5]/5 - PolyGamma[1/5]/5, 10, 105] // First

Prog

(PARI) Euler/5 + Pi/10*sqrt(1 + 2/sqrt(5)) + log(5)/20 + sqrt(5)/10*log((1 + sqrt(5))/2) \\ Michel Marcus, Apr 10 2015
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/5 + Pi(R)/10*Sqrt(1 + 2/Sqrt(5)) + Log(5)/20 + Sqrt(5)/10*Log((1 + Sqrt(5))/2); // G. C. Greubel, Aug 28 2018

Crossrefs

Cf. A001620 (EulerGamma), A016628, A200135, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

Sequence in context: A175452 A084714 A340820 * A360094 A030760 A329084

Adjacent sequences: A256776 A256777 A256778 * A256780 A256781 A256782

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 10 2015

Status

approved