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

Author

Jean-François Alcover, Aug 27 2015

Keywords

• nonn
• cons
• easy

Examples

			0.59072305644249473186595915351156205979836741723911440082771876593...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's MathWorld, Dirichlet Beta Function
• Wikipedia, Dirichlet beta function

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)).

Programs

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

PARI

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

Formula

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