A258814 Decimal expansion of the Dirichlet beta function of 7.

9, 9, 9, 5, 5, 4, 5, 0, 7, 8, 9, 0, 5, 3, 9, 9, 0, 9, 4, 9, 6, 3, 4, 6, 5, 4, 9, 8, 9, 9, 0, 5, 8, 9, 8, 3, 0, 0, 2, 1, 8, 8, 4, 8, 1, 9, 4, 9, 9, 7, 5, 7, 9, 2, 2, 5, 2, 6, 4, 9, 2, 1, 8, 9, 4, 1, 9, 0, 1, 1, 2, 1, 4, 4, 5, 9, 1, 1, 0, 5, 0, 0, 0, 6, 7, 5, 7, 8, 6, 6, 7, 9, 9, 5, 3, 6, 6, 4, 2, 0, 8, 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(7) = Sum_{n>=0} (-1)^n/(2n+1)^7 = (zeta(7, 1/4) - zeta(7, 3/4))/16384 = 61*Pi^7/184320.

Equals Product_{p prime >= 3} (1 - (-1)^((p-1)/2)/p^7)^(-1). - Amiram Eldar, Nov 06 2023

Example

0.9995545078905399094963465498990589830021884819499757922526492189419...

Mathematica

RealDigits[DirichletBeta[7], 10, 102] // First

Prog

(PARI) 61*Pi^7/184320 \\ Charles R Greathouse IV, Dec 06 2016
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 61*Pi(R)^7/184320; // 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)), A258815 (beta(8)), A258816 (beta(9)).

Sequence in context: A019897 A111613 A111591 * A346849 A146488 A051557

Adjacent sequences: A258811 A258812 A258813 * A258815 A258816 A258817

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 11 2015

Status

approved