1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finite series within finite series

  1. Feb 4, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to find a closed form for what at first light would be a straightforward finite series. Calculating it explicitly to a particular degree is not difficult, but I just can't find the closed form for the general case.

    2. Relevant equations
    For [tex]N>m[/tex], the series is:
    [tex]\sum_{k_m=1}^{N}(b^{m-1}x)^{k_m}\sum_{k_{m-1}=1}^{k_m}(b^{m-2}x)^{k_{m-2}}\cdots \sum_{k_2=1}^{k_3}(b x)^{k_2}\sum_{k_1=1}^{k_2}x^{k_2}[/tex]

    3. The attempt at a solution
    I know the answer will look something like this:
    [tex]\sum_{i=0}^{m}a_i(b,x) x^{i N}[/tex]
    where the [tex]a_i(b,x)[/tex] are linear combinations of b's and [tex]\frac{1}{1-(b^p x^r)^{-1}}[/tex], but I just can't find the general expression. Even a recurrence relation would be sufficient for my needs.

    Any help will be greatly appreciated.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads - Finite series within Date
Fourier sine series for a triangular wave on a finite string Mar 22, 2016
Z-Transform of finite series. Apr 9, 2015
Finite series Feb 12, 2014
Finite Series Expansion Jul 11, 2013
Finite series Mar 30, 2012