A239097 - OEIS

A239097

Decimal expansion of -(gamma-log(2))/2.

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

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OFFSET

0,2

COMMENTS

Decimal expansion of the generalized Euler constant -gamma(0,2).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

D. H. Lehmer, Euler constants for arithmetical progressions, Collection of articles in memory of Juriĭ Vladimirovič Linnik. Acta Arith. 27 (1975), 125--142. MR0369233 (51 #5468). See p. 128.

V. Ramaswami, Notes on Riemann's zeta-function, Journal of the London Mathematical Society, Vol. s1-9, No. 3 (1934), pp. 165-169. See p. 169, eq. (8).

FORMULA

From Amiram Eldar, Jun 30 2020: (Start)

Equals Sum_{k>=1} zeta(2*k+1)/((2*k+1)*2^(2*k+1)) (Ramaswami, 1934).

Equals Sum_{k>=1} arctanh(1/(2*k)) - 1/(2*k). (End)

Equals A255681 / 2. - Amiram Eldar, Oct 13 2025

EXAMPLE

0.057965757829206224405360015687887068516670399210165827657456...

MATHEMATICA

Join[{0}, RealDigits[(Log[2] - EulerGamma)/2, 10, 100][[1]]] (* G. C. Greubel, Aug 28 2018 *)

PROG

(PARI) (log(2)-Euler)/2 \\ Charles R Greathouse IV, Mar 25 2014

(Magma) SetDefaultRealField(RealField(100)); R:= RealField();