A261624 Decimal expansion of the Dirichlet beta function at 1/5.

5, 7, 3, 7, 1, 0, 8, 4, 7, 1, 8, 5, 9, 4, 6, 6, 4, 9, 3, 5, 7, 2, 6, 6, 5, 2, 7, 8, 3, 2, 0, 0, 4, 1, 7, 0, 4, 3, 6, 2, 4, 6, 9, 3, 8, 2, 4, 2, 6, 9, 0, 9, 3, 7, 6, 1, 8, 9, 5, 3, 6, 2, 8, 2, 5, 0, 7, 9, 2, 5, 3, 6, 1, 1, 2, 6, 5, 9, 4, 2, 1, 5, 7, 5, 0, 6, 2, 8, 3, 0, 1, 9, 3, 3, 1, 7, 4, 2, 4, 8, 8, 1

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(1/5) = (zeta(1/5, 1/4) - zeta(1/5, 3/4))/2^(2/5).

Example

0.57371084718594664935726652783200417043624693824269093761895362825...

Maple

evalf(Sum((-1)^n/(2*n+1)^(1/5), n=0..infinity), 120); # Vaclav Kotesovec, Aug 27 2015

Mathematica

RealDigits[DirichletBeta[1/5], 10, 102]//First

Prog

(PARI) beta(x)=(zetahurwitz(x, 1/4)-zetahurwitz(x, 3/4))/4^x
beta(.2) \\ Charles R Greathouse IV, Oct 18 2024

Crossrefs

Cf. A003881 (beta(1)=Pi/4), A006752 (beta(2)=Catalan), A153071 (beta(3)), A175572 (beta(4)), A175571 (beta(5)), A175570 (beta(6)), A261622 (beta(1/3)), A261623 (beta(1/4)).

Sequence in context: A019844 A155529 A374003 * A152081 A264736 A200620

Adjacent sequences: A261621 A261622 A261623 * A261625 A261626 A261627

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 27 2015

Status

approved