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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


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    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##.
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