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 A086279 Decimal expansion of 2nd Stieltjes constant gamma_2 (negated). 30
 0, 0, 9, 6, 9, 0, 3, 6, 3, 1, 9, 2, 8, 7, 2, 3, 1, 8, 4, 8, 4, 5, 3, 0, 3, 8, 6, 0, 3, 5, 2, 1, 2, 5, 2, 9, 3, 5, 9, 0, 6, 5, 8, 0, 6, 1, 0, 1, 3, 4, 0, 7, 4, 9, 8, 8, 0, 7, 0, 1, 3, 6, 5, 4, 5, 1, 8, 5, 0, 7, 5, 5, 3, 8, 2, 2, 8, 0, 4, 1, 4, 1, 7, 1, 9, 7, 8, 1, 9, 7, 3, 8, 1, 3, 7, 4, 5, 3, 7, 3, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 166. LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Stieltjes Constants Wikipedia, Stieltjes constants FORMULA Using the abbreviations a = log(z^2 + 1/4)/2, b = arctan(2*z) and c = cosh(Pi*z) then gamma_2 = -(Pi/3)*Integral_{0..infinity}(a^3-3*a*b^2)/c^2. The general case is for n >= 0 (which includes Euler's gamma as gamma_0) gamma_n = (-Pi/(n+1))* Integral_{0..infinity} sigma(n+1)/c^2, where sigma(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n,2*k)*b^(2*k)*a^(n-2*k). - Peter Luschny, Apr 19 2018 EXAMPLE -0.0096903... MAPLE evalf(gamma(2)); # R. J. Mathar, Feb 02 2011 MATHEMATICA Join[{0, 0}, RealDigits[N[-StieltjesGamma[2], 101]][[1]]] (* Jean-François Alcover, Oct 23 2012 *) N[4*EulerGamma^3 + Residue[Zeta[s]^4 / 2 - 2*EulerGamma*Zeta[s]^3, {s, 1}], 100] (* Vaclav Kotesovec, Jan 07 2017 *) CROSSREFS Cf. A001620, A082633, A086280, A086281, A086282, A183141, A183167, A183206, A184853, A184854. Sequence in context: A161484 A103985 A153071 * A155533 A083281 A019711 Adjacent sequences:  A086276 A086277 A086278 * A086280 A086281 A086282 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Jul 14 2003 STATUS approved

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Last modified October 14 12:45 EDT 2019. Contains 328006 sequences. (Running on oeis4.)