Results 1 to 2 of 2

Math Help - Bernoulli polynomials & Euler–Maclaurin summation

  1. #1
    Member Last_Singularity's Avatar
    Joined
    Dec 2008
    Posts
    157

    Bernoulli polynomials & Euler–Maclaurin summation

    Could you please point me in the right direction for this problem?

    Question: Use either Bernoulli polynomials or the Euler–Maclaurin summation formula to evaluate 1^4 + 2^4 + ... + n^4

    Thanks a lot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The Bernoulli polynomials are defined as...

    B_{k} (x) = \sum_{i=0}^{k} \binom {k}{i}\cdot B_{k-i}\cdot x^{i}

    where the B_{i} arer the 'Bernoulli numbers' defined in ricorsive manner as...

    B_{0}=1 , \sum_{i=0}^{k-1}\binom {k}{i}\cdot B_{i} =0

    The Bernoulli polynomial are useful [among other things...] for the following formula...

    \sum_{i=1}^{n} i^{k} = \frac {B_{k+1}(n+1) - B_{k+1}(0)}{k+1}

    Kind regards

     \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Summation Notation in Generalized Bernoulli Trials
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 22nd 2011, 04:00 PM
  2. Summation of Euler's φ-Function
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: July 8th 2010, 12:22 AM
  3. Replies: 2
    Last Post: February 2nd 2009, 07:41 AM
  4. Bernoulli and Euler Differential Equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: January 14th 2009, 09:08 AM
  5. Maclaurin polynomials
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 3rd 2008, 09:51 PM

Search Tags


/mathhelpforum @mathhelpforum