A258816 Decimal expansion of the Dirichlet beta function of 9.

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

G. C. Greubel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Dirichlet Beta Function.

Wikipedia, 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

Adjacent sequences: A258813 A258814 A258815 * A258817 A258818 A258819

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 11 2015

Status

approved