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A258815
Decimal expansion of the Dirichlet beta function of 8.
9
9, 9, 9, 8, 4, 9, 9, 9, 0, 2, 4, 6, 8, 2, 9, 6, 5, 6, 3, 3, 8, 0, 6, 7, 0, 5, 9, 2, 4, 0, 4, 6, 3, 7, 8, 1, 4, 7, 6, 0, 0, 7, 4, 3, 3, 0, 0, 7, 4, 2, 8, 0, 6, 9, 7, 2, 4, 9, 8, 7, 4, 2, 9, 2, 4, 0, 6, 7, 1, 1, 5, 9, 3, 2, 5, 0, 7, 1, 7, 3, 5, 1, 1, 2, 6, 4, 2, 7, 0, 5, 0, 8, 1, 3, 5, 7, 0, 4, 2, 6, 2, 1, 2, 8, 3
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Dirichlet Beta Function.
FORMULA
beta(8) = Sum_{n>=0} (-1)^n/(2n+1)^8 = (zeta(8, 1/4) - zeta(8, 3/4))/65536 = (PolyGamma(7, 1/4) - PolyGamma(7, 3/4))/330301440.
Equals ClausenFunction(8, Pi/2).
Equals Product_{p prime >= 3} (1 - (-1)^((p-1)/2)/p^8)^(-1). - Amiram Eldar, Nov 06 2023
EXAMPLE
0.99984999024682965633806705924046378147600743300742806972498742924...
MATHEMATICA
RealDigits[DirichletBeta[8], 10, 102] // First
PROG
(PARI) (zetahurwitz(8, 1/4)-zetahurwitz(8, 3/4))*(1/4)^8 \\ Hugo Pfoertner, Feb 07 2020
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)), A258816 (beta(9)).
Sequence in context: A346260 A019898 A330119 * A114054 A347220 A348294
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved