1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook