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A Closed form for series over Exponential Integral

  1. Feb 16, 2017 #1
    Is there a closed form for the constant given by:

    $$\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(2))}{n}$$

    (Where Ei is the exponential integral)?

    Could we generalize it for:

    $$I(k)=\sum_{n=2}^\infty \frac{Ei(-(n-1)\log(k))}{n}$$


    My try: As it is given that k will be a positive integer, I have already proved that these series converge at least for every k>1. To obtain a closed form, I have tried to substitute the exponential integral by both its main definition and its series expansion, with no success. Mathematica does not give any result either. Any help?
    Last edited: Feb 16, 2017
  2. jcsd
  3. Feb 23, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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