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

 

Logo

The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 A256684 A049005

Adjacent sequences:  A195100 A195101 A195102 * A195104 A195105 A195106

KEYWORD

nonn,cons

AUTHOR

R. J. Mathar, Sep 09 2011

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 August 28 13:11 EDT 2015. Contains 261122 sequences.