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A143298 Decimal expansion of Gieseking's constant. 19
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

Table of n, a(n) for n=1..105.

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

(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-Fran├žois 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

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 September 26 20:25 EDT 2016. Contains 276548 sequences.