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Simplify or clarify e^e^e^x ?

  1. Sep 15, 2010 #1
    Is there any way to simplify or clarify e^e^e^x ?
    Some sort of equivalence to a hypergeometric?
    How about e^e^x?
    Thanks
     
  2. jcsd
  3. Sep 15, 2010 #2

    CRGreathouse

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    Re: e^e^e^x

    Assuming that these associate the usual way (right-to-left), they don't really simplify.
     
  4. Sep 16, 2010 #3

    HallsofIvy

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    Re: e^e^e^x

    What you have written, without parentheses,is ambiguous. That is why CRGreathouse said "Assuming that these associate the usual way (right-to-left)".

    [tex]e^{e^{e^x}}[/tex]
    does not simplify.

    [tex]((e^e)^e)^x= (e^e)^{ex}= e^{e^2x}[/tex]
     
  5. Sep 16, 2010 #4
    Re: e^e^e^x

    Assume it's the way I think you want it to be:

    [tex]e^{e^{e^{x}}}=\sum_{n=0}^{\infty} a_n x^n[/tex]

    and you know how to figure out what each a_n is.
     
  6. Sep 17, 2010 #5
    Re: e^e^e^x

    Thanks everyone for your help. Yes, I meant

    [tex]e^{e^{e^{x}}}[/tex]
     
    Last edited: Sep 17, 2010
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