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 A175572 Decimal expansion of the Dirichlet beta function of 4. 10
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the value of the Dirichlet L-series 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 G. C. Greubel, Table of n, a(n) for n = 0..10000 Richard J. Mathar, Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015. Wikipedia, Dirichlet beta function FORMULA Equals Sum_{n>=1} A101455(n)/n^4. [corrected by R. J. Mathar, Feb 01 2018] Also equals (PolyGamma(3, 1/4) - PolyGamma(3, 3/4))/1536. - Jean-François Alcover, Jun 11 2015 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 RealDigits[ DirichletBeta[4], 10, 105] // First (* Jean-François Alcover, Feb 11 2013, updated Mar 14 2018 *) PROG (PARI) beta(x)=(zetahurwitz(x, 1/4)-zetahurwitz(x, 3/4))/4^x beta(4) \\ Charles R Greathouse IV, Jan 31 2018 CROSSREFS Cf. A003881 (at 1), A006752 (at 2), A153071 (at 3). Sequence in context: A195477 A157680 A011228 * A263984 A021095 A090998 Adjacent sequences:  A175569 A175570 A175571 * A175573 A175574 A175575 KEYWORD cons,easy,nonn,changed AUTHOR R. J. Mathar, Jul 15 2010 STATUS approved

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Last modified April 19 18:54 EDT 2018. Contains 302748 sequences. (Running on oeis4.)