Results 1 to 2 of 2

Math Help - Summation of an Infinite Series

  1. #1
    Member sbhatnagar's Avatar
    Joined
    Sep 2011
    From
    New Delhi, India
    Posts
    200
    Thanks
    17

    Summation of an Infinite Series

    Show that

    \sum_{n=1}^\infty \frac{\zeta(2n)}{n 2^{2n}} = \ln \left( \frac{\pi}{2}\right)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2012
    From
    sanaa
    Posts
    18
    Thanks
    3

    Re: Summation of an Infinite Series

    I used the equality : \Gamma(s) \zeta(s) = \int^{\infty}_0 \frac{t^{s-1}}{e^t-1}\,dt

    and got \,2\int^{\infty}_0 \frac{\cosh(\frac{t}{2})-1}{t(e^t-1)}\, dt

    I am still trying to find this integral ,
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 21st 2011, 08:55 AM
  2. Help with infinite Summation
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: November 7th 2010, 07:18 PM
  3. finding value of summation of infinite series
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 4th 2010, 04:23 AM
  4. Infinite summation
    Posted in the Statistics Forum
    Replies: 0
    Last Post: January 18th 2010, 12:55 PM
  5. Please check summation of infinite series?
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 18th 2009, 10:30 PM

Search Tags


/mathhelpforum @mathhelpforum