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 A256780 Decimal expansion of the generalized Euler constant gamma(2,5). 10
 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 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/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 (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), 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-François Alcover, Apr 10 2015 STATUS approved

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Last modified December 9 17:51 EST 2018. Contains 318023 sequences. (Running on oeis4.)