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A256779
Decimal expansion of the generalized Euler constant gamma(1,5).
11
7, 3, 5, 9, 2, 0, 3, 9, 6, 8, 3, 1, 6, 1, 7, 5, 8, 4, 1, 8, 9, 2, 8, 9, 7, 2, 5, 8, 4, 4, 7, 5, 2, 8, 9, 3, 0, 5, 9, 9, 9, 7, 3, 8, 3, 9, 8, 7, 6, 2, 5, 0, 1, 7, 6, 5, 2, 6, 4, 2, 1, 5, 4, 5, 4, 3, 4, 8, 9, 1, 5, 3, 2, 7, 6, 7, 9, 2, 3, 7, 7, 5, 8, 3, 2, 8, 8, 7, 8, 9, 2, 4, 5, 2, 7, 8, 1, 5, 0, 3, 2, 2, 4, 8, 8
OFFSET
0,1
LINKS
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).
Equals Sum_{n>=0} (1/(5n+1) - 2/5*arctanh(5/(10n+7))).
Equals -(psi(1/5) + log(5))/5 = (A200135 - A016628)/5. - Amiram Eldar, Jan 07 2024
EXAMPLE
0.735920396831617584189289725844752893059997383987625...
MATHEMATICA
RealDigits[-Log[5]/5 - PolyGamma[1/5]/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), A016628, A200135, A228725 (gamma(1,2)), A256425 (gamma(1,3)), A256778-A256784 (selection of ruler-and-compass constructible gamma(r,k)).
Sequence in context: A175452 A084714 A340820 * A360094 A030760 A329084
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved