OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Philippe Flajolet, Bruno Salvy, Euler Sums and Contour Integral Representations, Experimental Mathematics 7:1 (1998) page 27.
FORMULA
Equals -37/7560*Pi^6*zeta(3) + zeta(3)^3 - 11/120*Pi^4*zeta(5) + 1/2*Pi^2*zeta(7) + 197/24*zeta(9).
EXAMPLE
0.02289126788224074913774364071997743746511359015190275216397993401922...
MATHEMATICA
RealDigits[197/24*Zeta[9] - 33/4*Zeta[4]*Zeta[5] - 37/8*Zeta[3]*Zeta[6] + Zeta[3]^3 + 3*Zeta[2]*Zeta[7], 10, 104] // First // Prepend[#, 0]&
PROG
(PARI) default(realprecision, 100); -37/7560*Pi^6*zeta(3) + zeta(3)^3 - 11/120*Pi^4*zeta(5) + 1/2*Pi^2*zeta(7) + 197/24*zeta(9) \\ G. C. Greubel, Aug 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); L:=RiemannZeta(); -(37/7560)*Pi(R)^6*Evaluate(L, 3) + Evaluate(L, 3)^3 - (11/120)*Pi(R)^4*Evaluate(L, 5) + Pi(R)^2*Evaluate(L, 7)/2 + (197/24)*Evaluate(L, 9); // G. C. Greubel, Aug 31 2018
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 04 2014
STATUS
approved