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A175570 Decimal expansion of the Dirichlet beta function of 6. 7
9, 9, 8, 6, 8, 5, 2, 2, 2, 2, 1, 8, 4, 3, 8, 1, 3, 5, 4, 4, 1, 6, 0, 0, 7, 8, 7, 8, 6, 0, 2, 0, 6, 5, 4, 9, 6, 7, 8, 3, 6, 4, 5, 4, 6, 1, 2, 6, 5, 1, 4, 4, 1, 1, 4, 0, 4, 1, 2, 6, 4, 5, 1, 2, 2, 9, 7, 1, 2, 7, 5, 2, 5, 5, 9, 0, 3, 1, 0, 8, 9, 4, 5, 5, 4, 8, 2, 1, 8, 4, 5, 3, 8, 6, 2, 9, 7, 9, 7, 8, 4, 0, 7, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The beta function of arguments 1 to 3 is A003881, A006752 and A153071.

REFERENCES

L. B. W. Jolley, Summation of Series, Dover (1971) eq. 308.

LINKS

Table of n, a(n) for n=0..104.

Wikipedia, Dirichlet beta function.

FORMULA

Equals sum_{n>=1} 1/A101455(n)^6. [see arxiv1008.2547, L(m=4,r=2,s=6)]

Also equals (PolyGamma(5, 1/4) - PolyGamma(5, 3/4))/491520. - Jean-François Alcover, Jun 11 2015

EXAMPLE

0.998685222218438135441600...

MAPLE

DirichletBeta := proc(s) 4^(-s)*(Zeta(0, s, 1/4)-Zeta(0, s, 3/4)) ; end proc: x := DirichletBeta(6) ; x := evalf(x) ;

MATHEMATICA

DirichletBeta[x_] := (Zeta[x, 1/4] - Zeta[x, 3/4])/4^x; RealDigits[ DirichletBeta[6], 10, 105] // First (* Jean-François Alcover, Feb 11 2013 *)

CROSSREFS

Sequence in context: A051554 A146493 A019896 * A050812 A139345 A231470

Adjacent sequences:  A175567 A175568 A175569 * A175571 A175572 A175573

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Jul 15 2010

STATUS

approved

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Last modified December 7 23:03 EST 2016. Contains 278900 sequences.