# How to solve this functional (recurrence) equation ?

by jk22
Tags: equation, functional, recurrence, solve
 P: 136 I'm in a problem where I have to solve the following functional equation : $$F(n)^2=n+F(n+1)$$ 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_...l#Square_roots
 Sci Advisor P: 5,941 Don't know of a method. As stated the problem is incomplete - you need an initial condition (F(0) = ?).
 P: 136 The problem is to find F(1), knowing that $$F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$$.
HW Helper
P: 3,436

## How to solve this functional (recurrence) equation ?

 Quote by jk22 The problem is to find F(1), knowing that $$F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$$.
Should that be to find F(n) given that $F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$ ?

Find F(2) and the pattern becomes clear.

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