login
A258814
Decimal expansion of the Dirichlet beta function of 7.
10
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
Eric Weisstein's World of Mathematics, 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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved