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/8 + 1/8*(Pi/2*(sqrt(2)+1) + log(2) + sqrt(2)*log(sqrt(2) + 1)).
Equals Sum_{n>=0} (1/(8n+1) - 1/4*arctanh(4/(8n+5))).
EXAMPLE
0.788631390202002367443880819838976661978118204921...
MATHEMATICA
RealDigits[-3/8*Log[2] - PolyGamma[1/8]/8, 10, 105] // First
PROG
(PARI) Euler/8 + 1/8*(Pi/2*(sqrt(2)+1) + log(2) + sqrt(2)*log(sqrt(2) + 1)) \\ Michel Marcus, Apr 10 2015
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); EulerGamma(R)/8 + (1/8)*(Pi(R)/2*(Sqrt(2)+1) + Log(2) + Sqrt(2)*Log(Sqrt(2) + 1)); // G. C. Greubel, Aug 28 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 10 2015
STATUS
approved