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A256780 Decimal expansion of the generalized Euler constant gamma(2,5). 9
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

Table of n, a(n) for n=0..104.

D. H. Lehmer, Euler constants for arithmetic progressions, Acta Arith. 27 (1975) p. 134.

FORMULA

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

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 January 19 22:02 EST 2018. Contains 297938 sequences.