How to solve this functional (recurrence) equation ?by jk22 Tags: equation, functional, recurrence, solve 

#1
Nov1613, 10:18 AM

P: 133

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_...l#Square_roots 



#2
Nov1613, 03:56 PM

Sci Advisor
P: 5,935

Don't know of a method. As stated the problem is incomplete  you need an initial condition (F(0) = ?).




#3
Nov1713, 02:32 AM

P: 133

The problem is to find F(1), knowing that [tex]F(1)=\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}[/tex].




#4
Nov1713, 05:42 AM

HW Helper
P: 3,436

How to solve this functional (recurrence) equation ?Find F(2) and the pattern becomes clear. 


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