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 A143298 Decimal expansion of Gieseking's constant. 20
 1, 0, 1, 4, 9, 4, 1, 6, 0, 6, 4, 0, 9, 6, 5, 3, 6, 2, 5, 0, 2, 1, 2, 0, 2, 5, 5, 4, 2, 7, 4, 5, 2, 0, 2, 8, 5, 9, 4, 1, 6, 8, 9, 3, 0, 7, 5, 3, 0, 2, 9, 9, 7, 9, 2, 0, 1, 7, 4, 8, 9, 1, 0, 6, 7, 7, 6, 5, 9, 7, 4, 7, 6, 2, 5, 8, 2, 4, 4, 0, 2, 2, 1, 3, 6, 4, 7, 0, 3, 5, 4, 2, 2, 8, 2, 5, 6, 6, 9, 4, 9, 4, 5, 8, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES J. Borwein and P. Borwein, Experimental and computational mathematics: Selected writings, Perfectly Scientific Press, 2010, p. 106. Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 233. LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 C. C. Adams, The newest inductee in the Number Hall of Fame, Math. Mag., 71 (1998), 341-349. P. J. de Doelder, On the Clausen integral Cl_2(theta) and a related integral, J. Comp. Appl. Math. 11 (1984) 325-330. K. S. Kolbig, Chebyshev coefficients for the Clausen function Cl_2(x), J. Comp. Appl. Math. 64 (1995) 295-297. Eric Weisstein's World of Mathematics, Gieseking's Constant FORMULA Equals (9 - PolyGamma(1, 2/3) + PolyGamma(1, 4/3))/(4*sqrt(3)). Equals Sum_{k>0} sin(k*Pi/3)/k^2; (also equals (sqrt(3)/2)*Sum_{k>=1} -1/(6k-1)^2 - 1/(6k-2)^2 + 1/(6k-4)^2 + 1/(6k-5)^2). - Jean-François Alcover, Jun 19 2016, from the book by J. & P. Borwein. EXAMPLE 1.0149416064096536250... MAPLE sqrt(3)/6*(Psi(1, 1/3)-2*Pi^2/3) ; evalf(%) ; # R. J. Mathar, Sep 23 2013 MATHEMATICA N[(9 - PolyGamma[1, 2/3] + PolyGamma[1, 4/3])/(4*Sqrt[3]), 105] // RealDigits // First PROG (PARI) polygamma(n, x) = if (n == 0, psi(x), (-1)^(n+1)*n!*zetahurwitz(n+1, x)); sqrt(3)/6*(polygamma(1, 1/3) - 2*Pi^2/3) (9 - polygamma(1, 2/3) + polygamma(1, 4/3))/(4*sqrt(3)) \\ Gheorghe Coserea, Sep 30 2018 (PARI) clausen(n, x) = my(z = polylog(n, exp(I*x))); if (n%2, real(z), imag(z)); clausen(2, Pi/3) \\ Gheorghe Coserea, Sep 30 2018 (PARI) sqrt(3)/2 * sumpos(n=1, 1/(6*n-4)^2 + 1/(6*n-5)^2 - 1/(6*n-1)^2 - 1/(6*n-2)^2) \\ Gheorghe Coserea, Sep 30 2018 CROSSREFS Sequence in context: A178143 A070435 A070516 * A177839 A013669 A085365 Adjacent sequences:  A143295 A143296 A143297 * A143299 A143300 A143301 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Aug 05 2008 STATUS approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)