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A256780 Decimal expansion of the generalized Euler constant gamma(2,5). 10
1, 9, 0, 3, 8, 9, 3, 2, 6, 4, 3, 0, 2, 0, 3, 1, 5, 4, 2, 2, 5, 9, 8, 3, 2, 2, 9, 7, 6, 4, 2, 6, 8, 1, 6, 3, 2, 6, 0, 1, 5, 1, 9, 4, 8, 4, 4, 8, 4, 5, 8, 4, 8, 7, 0, 6, 4, 2, 6, 1, 1, 5, 6, 7, 4, 7, 6, 8, 6, 4, 1, 1, 0, 4, 4, 5, 7, 6, 7, 2, 3, 8, 6, 8, 4, 0, 5, 3, 6, 2, 8, 5, 2, 0, 8, 6, 8, 4, 1, 3, 2, 2, 5, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
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/5 + Pi/10*sqrt(1 - 2/sqrt(5)) + log(5)/20 - sqrt(5)/10*log((1 + sqrt(5))/2).

Sum_{n>=0} (1/(5n+2) - 2/5*arctanh(5/(10n+9))).

EXAMPLE

0.190389326430203154225983229764268163260151948448458487...

MATHEMATICA

RealDigits[-Log[5]/5 - PolyGamma[2/5]/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), A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).

Sequence in context: A211884 A154464 A202344 * A094452 A154705 A197389

Adjacent sequences:  A256777 A256778 A256779 * A256781 A256782 A256783

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Apr 10 2015

STATUS

approved

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Last modified September 19 19:56 EDT 2018. Contains 315217 sequences. (Running on oeis4.)