How to solve this functional (recurrence) equation ?

  1. I'm in a problem where I have to solve the following functional equation :

    [tex]F(n)^2=n+F(n+1)[/tex]

    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. mathman

    mathman 6,465
    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 3,690
    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.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?

0
Draft saved Draft deleted