

A256778


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


15



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
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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))).


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), A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256779A256784 (selection of rulerandcompass 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

JeanFrançois Alcover, Apr 10 2015


STATUS

approved



