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A195103 Decimal expansion of the Dirichlet beta-function at 1/2. 0
6, 6, 7, 6, 9, 1, 4, 5, 7, 1, 8, 9, 6, 0, 9, 1, 7, 6, 6, 5, 8, 6, 9, 0, 9, 2, 9, 3, 0, 0, 2, 4, 8, 4, 8, 2, 2, 5, 1, 5, 9, 7, 8, 2, 9, 7, 4, 2, 9, 3, 7, 0, 9, 7, 7, 4, 9, 7, 9, 8, 6, 5, 7, 3, 2, 1, 7, 6, 1, 6, 0, 8, 7, 8, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Appears in lattice sums like A088537.

LINKS

Table of n, a(n) for n=0..74.

Wikipedia, Dirichlet beta function

FORMULA

Equals (zeta(1/2,1/4)-zeta(1/2,3/4))/2 where zeta(.,.) is the Hurwitz zeta-function

EXAMPLE

Equals 0.66769145718960917665869...

MAPLE

DirichletBeta := proc(s) (Zeta(0, s, 1/4)-Zeta(0, s, 3/4))/4^s ; end proc:

x := evalf(DirichletBeta(1/2)) ;

MATHEMATICA

DirichletBeta[x_] := (Zeta[x, 1/4] - Zeta[x, 3/4])/4^x; RealDigits[ DirichletBeta[1/2], 10, 75] // First (* Jean-François Alcover, Feb 20 2013 *)

CROSSREFS

Sequence in context: A070058 A160057 A190145 * A152485 A049005 A198987

Adjacent sequences:  A195100 A195101 A195102 * A195104 A195105 A195106

KEYWORD

nonn,cons

AUTHOR

R. J. Mathar, Sep 09 2011

STATUS

approved

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Last modified April 19 17:22 EDT 2014. Contains 240763 sequences.