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A sum involving binomial coefficient

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

    latex2png.2.php?z=100&eq=%5Csum_%7Bi%3Dk%7D%5E%7Bn%7D%20%7Bi%20%5Cchoose%20k%7D%20i%5E%7B-t%7D.jpg


    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).
     
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