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Good afternoon

The euler number is a irrational number. And you can have a infinite continued fraction of euler number. But how can you form the coninued fraction of euler number?

Gianna
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  • See https://en.wikipedia.org/wiki/List_of_representations_of_e#As_a_continued_fraction – lhf Sep 26 '18 at 17:29
  • http://www.wolframalpha.com/input/?i=continued+fraction+of+euler+number – vadim123 Sep 26 '18 at 17:30
  • Well, if you have a decimal expansion out to sufficiently many places, you can at least get the first few partial denominators in the regular continued fraction. One can do that for any real number at all. – Lubin Sep 26 '18 at 17:41
  • Euler surely deserves a capital letter. Anyway, you may derive the continued fraction of $e$ from the Beuker integrals $\int_{0}^{1}x^n(1-x)^m e^{-x},dx$ or from the Gauss continued fraction for $\tanh$. Have a look at the last pages of my notes for further details. – Jack D'Aurizio Sep 26 '18 at 18:08

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