A261623 Decimal expansion of the Dirichlet beta function at 1/4.

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

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

Example

0.59072305644249473186595915351156205979836741723911440082771876593...

Maple

evalf(Sum((-1)^n/(2*n+1)^(1/4), n=0..infinity), 120); # Vaclav Kotesovec, Aug 27 2015

Mathematica

RealDigits[DirichletBeta[1/4], 10, 103]//First

Prog

(PARI) beta(x)=(zetahurwitz(x, 1/4)-zetahurwitz(x, 3/4))/4^x
beta(1/4) \\ 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)), A261624 (beta(1/5)).

Sequence in context: A277651 A096789 A342714 * A298515 A306778 A019705

Adjacent sequences: A261620 A261621 A261622 * A261624 A261625 A261626

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 27 2015

Status

approved