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A258814 Decimal expansion of the Dirichlet beta function of 7. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Eric Weisstein's MathWorld, 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.

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 * A146488 A051557 A146491

Adjacent sequences:  A258811 A258812 A258813 * A258815 A258816 A258817

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Jun 11 2015

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)