login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A175571 Decimal expansion of the Dirichlet beta function of 5. 0
9, 9, 6, 1, 5, 7, 8, 2, 8, 0, 7, 7, 0, 8, 8, 0, 6, 4, 0, 0, 6, 3, 1, 9, 3, 6, 8, 6, 3, 0, 9, 7, 5, 2, 8, 1, 5, 1, 1, 3, 9, 5, 5, 2, 9, 3, 8, 8, 2, 6, 4, 9, 4, 3, 2, 0, 7, 9, 8, 3, 2, 1, 5, 1, 2, 4, 4, 6, 2, 8, 6, 5, 0, 1, 8, 2, 7, 4, 8, 1, 9, 2, 8, 9, 6, 5, 9, 8, 3, 2, 2, 7, 0, 5, 2, 4, 4, 7, 5, 5, 9, 9, 0, 8, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The value of the Dirichlet L-series L(m=4,r=2,s=4), see arXiv:1008.2547.

REFERENCES

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

LINKS

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

Wikipedia, Dirichlet beta function.

FORMULA

Equals 5*Pi^5/1536 = sum_{n>=1} 1/A101455(n)^5, where Pi^5 = A092731 .

Also equals sum_{n>=0} (-1)^n/(2*n+1)^5 [Jean-François Alcover, Mar 29 2013]

EXAMPLE

0.99615782807708806400631936...

MAPLE

DirichletBeta := proc(s) 4^(-s)*(Zeta(0, s, 1/4)-Zeta(0, s, 3/4)) ; end proc: x := DirichletBeta(5) ; x := evalf(x) ;

MATHEMATICA

DirichletBeta[x_] := (Zeta[x, 1/4] - Zeta[x, 3/4])/4^x; RealDigits[ DirichletBeta[5], 10, 105] // First (* Jean-François Alcover, Feb 20 2013 *)

CROSSREFS

Sequence in context: A136130 A144668 A021505 * A019894 A157293 A146487

Adjacent sequences:  A175568 A175569 A175570 * A175572 A175573 A175574

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Jul 15 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 26 08:46 EST 2014. Contains 250021 sequences.