A295874 Decimal expansion of the real positive fixed point of the Dirichlet beta function.

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

Offset: 0

Author

Michal Paulovic, Dec 31 2017

Keywords

• nonn
• cons

Examples

			0.72656419327404362644162413010113341550433084723912002242028410346454317481...
		

Links

• Eric Weisstein's MathWorld, Dirichlet Beta Function.
• Wikipedia, Dirichlet beta function.

Crossrefs

Cf. A261624.

Programs

Maple

Digits:= 140:
f:= s-> sum((-1)^n/(2*n+1)^s, n=0..infinity):
fsolve(f(x)=x, x);  # Alois P. Heinz, Feb 05 2018

Mathematica

RealDigits[ FindRoot[ DirichletBeta[x] == x, {x, 0}, WorkingPrecision -> 2^7, AccuracyGoal -> 2^8, PrecisionGoal -> 2^7][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2018 *)

PARI

solve(x=0,1,sumalt(n=0,((-1)^n)/(2*n+1)^x)-x)