1. Limited time only! Sign up for a free 30min personal 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!

Power series representation

  1. Nov 3, 2013 #1
    Hi, I'm trying to find the series representation of [tex] f(x)=\int_{0}^{x} \frac{e^{t}}{1+t}dt [/tex]. I have found it ussing the Maclaurin series, differenciating multiple times and finding a pattern. But I think it must be an eassier way, using the power series of elementary functions. I know that [tex]e^{x}=\sum_{0}^{\infty}\frac{x^{n}}{n!}[/tex] and [tex]\frac{1}{1+x}=\sum_{}^{\infty}(-1)^{n}x^{n}[/tex] but I don't know how to use it here. Thanks

    (Don't hesitate to correct my english)
  2. jcsd
  3. Nov 3, 2013 #2


    User Avatar
    Science Advisor

    If ##f(x) = \sum_{n=0}^\infty a_n x^n## then
    ##\frac{f}{1-x} = \sum_{n=0}^\infty \sum_{j=0}^n a_j x^n##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook