|
|
A197070
|
|
Decimal expansion of the Dirichlet eta-function at 3.
|
|
14
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Wikipedia, Dirichlet eta function.
|
|
FORMULA
|
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
|
|
EXAMPLE
|
0.9015426773696957140498036211335874930737...
|
|
MAPLE
|
3*Zeta(3)/4 ; evalf(%) ;
|
|
MATHEMATICA
|
RealDigits[3(Zeta[3])/4, 10, 75][[1]] (* Bruno Berselli, Dec 20 2011 *)
|
|
PROG
|
(PARI) -polylog(3, -1) \\ Charles R Greathouse IV, Mar 28 2012
(PARI) 3/4*zeta(3) \\ Charles R Greathouse IV, Mar 28 2012
|
|
CROSSREFS
|
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
|
|
KEYWORD
|
cons,easy,nonn
|
|
AUTHOR
|
R. J. Mathar, Oct 09 2011
|
|
STATUS
|
approved
|
|
|
|