How to solve this functional (recurrence) equation ?

  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 :
  2. jcsd
  3. mathman

    mathman 6,750
    Science Advisor
    Gold Member

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

    Mentallic 3,783
    Homework Helper

    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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