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A258816
Decimal expansion of the Dirichlet beta function of 9.
10
9, 9, 9, 9, 4, 9, 6, 8, 4, 1, 8, 7, 2, 2, 0, 0, 8, 9, 8, 2, 1, 3, 5, 8, 8, 7, 3, 2, 9, 3, 8, 4, 7, 5, 2, 7, 3, 7, 2, 7, 4, 7, 9, 9, 6, 9, 1, 7, 9, 6, 1, 6, 0, 1, 2, 2, 3, 1, 6, 2, 7, 2, 3, 0, 8, 2, 9, 7, 8, 6, 5, 1, 3, 7, 9, 0, 4, 8, 5, 6, 3, 8, 8, 6, 1, 7, 1, 3, 9, 0, 2, 5, 8, 3, 2, 6, 5, 2, 9, 7, 3, 0, 7, 8
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Dirichlet Beta Function.
FORMULA
beta(9) = Sum_{n>=0} (-1)^n/(2n+1)^9 = (zeta(9, 1/4) - zeta(9, 3/4))/262144 = 277*Pi^9/8257536.
Equals Product_{p prime >= 3} (1 - (-1)^((p-1)/2)/p^9)^(-1). - Amiram Eldar, Nov 06 2023
EXAMPLE
0.999949684187220089821358873293847527372747996917961601223162723...
MATHEMATICA
RealDigits[DirichletBeta[9], 10, 104] // First
PROG
(PARI) default(realprecision, 100); 277*Pi^9/8257536 \\ G. C. Greubel, Aug 24 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 277*Pi(R)^9/8257536; // G. C. Greubel, Aug 24 2018
CROSSREFS
Cf. A003881 (beta(1)=Pi/4), A006752 (beta(2)=Catalan), A153071 (beta(3)), A175572 (beta(4)), A175571 (beta(5)), A175570 (beta(6)), A258814 (beta(7)), A258815 (beta(8)).
Sequence in context: A346450 A102819 A111664 * A291430 A146494 A111691
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved