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How to solve this functional (recurrence) equation ?

  1. Nov 16, 2013 #1
    I'm in a problem where I have to solve the following functional equation :


    Does anyone know some methods to solve this kind of problems ?

    A similar equation happens in Ramanujan example of root denesting : http://en.wikipedia.org/wiki/Nested_radical#Square_roots
  2. jcsd
  3. Nov 16, 2013 #2


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    Don't know of a method. As stated the problem is incomplete - you need an initial condition (F(0) = ?).
  4. Nov 17, 2013 #3
    The problem is to find F(1), knowing that [tex]F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}[/tex].
  5. Nov 17, 2013 #4


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    Should that be to find F(n) given that [itex]F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}[/itex] ?

    Find F(2) and the pattern becomes clear.
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