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

0,1

Links

Table of n, a(n) for n=0..106.

Eric Weisstein's MathWorld, Dirichlet Beta Function.

Wikipedia, Dirichlet beta function.

Example

0.72656419327404362644162413010113341550433084723912002242028410346454317481...

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 *)

Prog

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

Crossrefs

Cf. A261624.

Sequence in context: A225444 A175408 A019934 * A182548 A322933 A143306

Adjacent sequences: A295871 A295872 A295873 * A295875 A295876 A295877

Keyword

nonn,cons

Author

Michal Paulovic, Dec 31 2017

Status

approved