Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A sum involving binomial coefficient

  1. Jul 22, 2010 #1
    [tex]sum_{i=k}^{n} {i \choose k}i^{-t}[/tex]


    where t is a constant.

    Does it have a closed form?
    Last edited: Jul 22, 2010
  2. jcsd
  3. Jul 27, 2010 #2
    A closed form is possible only for integral values of t (that too, if you can solve the differential equation involving the generating function).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook