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A197070
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Decimal expansion of the Dirichlet eta-function at 3.
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14
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9, 0, 1, 5, 4, 2, 6, 7, 7, 3, 6, 9, 6, 9, 5, 7, 1, 4, 0, 4, 9, 8, 0, 3, 6, 2, 1, 1, 3, 3, 5, 8, 7, 4, 9, 3, 0, 7, 3, 7, 3, 9, 7, 1, 9, 2, 5, 5, 3, 7, 4, 1, 6, 1, 3, 4, 4, 2, 0, 3, 6, 6, 6, 5, 0, 6, 3, 7, 8, 6, 5, 4, 3, 3, 9
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OFFSET
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0,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Wikipedia, Dirichlet eta function.
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FORMULA
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Equals 3*zeta(3)/4 = 3*A002117/4.
Also equals the integral over the unit cube [0,1]x[0,1]x[0,1] of 1/(1+x*y*z) dx dy dz. - Jean-François Alcover, Nov 24 2014
Equals Sum_{n>=1} (-1)^(n+1)/n^3. - Terry D. Grant, Aug 03 2016
Equals Lim_{n -> infinity} A136675(n)/A334582(n). - Petros Hadjicostas, May 07 2020
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EXAMPLE
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0.9015426773696957140498036211335874930737...
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MAPLE
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3*Zeta(3)/4 ; evalf(%) ;
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MATHEMATICA
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RealDigits[3(Zeta[3])/4, 10, 75][[1]] (* Bruno Berselli, Dec 20 2011 *)
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PROG
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(PARI) -polylog(3, -1) \\ Charles R Greathouse IV, Mar 28 2012
(PARI) 3/4*zeta(3) \\ Charles R Greathouse IV, Mar 28 2012
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CROSSREFS
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Cf. A002117 (zeta(3)), A072691, A136675, A233090 (5*zeta(3)/8), A233091 (7*zeta(3)/8), A072691, A334582.
Sequence in context: A021530 A272232 A110909 * A197333 A226120 A244593
Adjacent sequences: A197067 A197068 A197069 * A197071 A197072 A197073
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KEYWORD
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cons,easy,nonn
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AUTHOR
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R. J. Mathar, Oct 09 2011
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STATUS
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approved
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