1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    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!

Bernoulli Recursions

  1. Jan 10, 2008 #1
    I don't know if this is appropriate or not, here or anywhere. However, I propose this thread be used to post recursive formula for the Bernoulli numbers. It saves a great deal of frustration.
    The first is simply,

    [tex] \sum_{k = 0}^{n-1} \binom{n}{k} B_{k} = 0 [/tex]
     
  2. jcsd
  3. Jan 11, 2008 #2

    Gib Z

    User Avatar
    Homework Helper

  4. Jan 11, 2008 #3
    One of the first places I tried, maybe it'll be better if I'm a bit more specific- I need to show that,
    [tex] (1 - 2^{2k}) B_{2k} = \sum_{r = 1}^{k} B_{2(k-r)} \binom{2k}{2r} (2^{2(k-r) - 1} - 1) [/tex]
    (should be right...)
    Tried a few approaches, didn't work, I might not be trying hard enough(bit of a hectic period), I'd sure appreciate some help! A nod in the right direction even.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Bernoulli Recursions
  1. Notation for recursion (Replies: 3)

  2. Recursive question (Replies: 1)

  3. Integral: recursion (Replies: 12)

  4. Simple recursion (Replies: 3)

Loading...