

A175572


Decimal expansion of the Dirichlet beta function of 4.


1



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

0,1


COMMENTS

The beta function of arguments 1 to 3 are A003881, A006752 and A153071.
This is the value of the Dirichlet Lseries for A101455 at s=4, see arXiv:1008.2547, L(m=4,r=2,s=4).


REFERENCES

L. B. W. Jolley, Summation of Series, Dover (1961) eq (308).


LINKS

Table of n, a(n) for n=0..104.
Anonymous, Dirichlet beta function, Wikipedia


FORMULA

Equals sum_{n>=1} 1/A101455(n)^4.


EXAMPLE

0.988944551741105336108422633...


MAPLE

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


MATHEMATICA

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


CROSSREFS

Sequence in context: A195477 A157680 A011228 * A021095 A090998 A163930
Adjacent sequences: A175569 A175570 A175571 * A175573 A175574 A175575


KEYWORD

cons,easy,nonn


AUTHOR

R. J. Mathar, Jul 15 2010


STATUS

approved



