Strange, I calculated manually with excel the first 10 series:
I got: 3.128171204
D2= 1.6180339887 (phi)
=RADQ(D2+2*RADQ(D2+3*RADQ(D2+4*RADQ(D2+5*RADQ(D2+6*RADQ(D2+7*RADQ(D2+8*RADQ(D2+9*RADQ(D2+10))))))))
I calculated that for phi (Golden section)
f(0)=2.267712876
But it is not correct:
http://www.wolframalpha.com/input/?i=f\left(n+1\right)=\frac{1}{1.6180339887}\left(f\left(n\right)^2-n-1\right);+f(0)=+2.267712876
What's wrong?
oh, my error ignores...
Question, if I want to replace (retaining the formula) only the pi with phi example, and doing all the calculations as we did together should work?
##\large{\sqrt{2+\phi \sqrt{3+\phi\sqrt{4+\phi\sqrt{5+\dotsb}}}}}##
well, understood thank you very much!
Last question just to understand:
f(0)= 3.609993083
http://www.wolframalpha.com/input/?i=f%5Cleft(n%2B1%5Cright)%3D%5Cfrac%7B1%7D%7B%5Cpi%7D%5Cleft(f%5Cleft(n%5Cright)%5E2-n-1%5Cright);+f(0)%3D+3.609993083
##\sqrt{2+\pi }## f(0) should not give 2.26751...
I am really happy that it works, after days of work.
Thanks for the explanations, you have a great talent.
You asked me if I can generate f(9,000) in MatLab, the answer is no, do you want to explain it to me? That would be the culmination of the project.
well now I've understood the situation,
I have to find the key value of f0), but I'm currently struggling a lot, if you're patient and want to I'd like if together you help me to calculate the value of f(0). I would be very grateful.
I am a looking for a recursive formula in the form of:
##f\left(n\right)=\sqrt{n+1+\pi f\left(n+1\right)}##
in alternative
##f\left(n+1\right)=\frac{1}{\pi}\left(f\left(n\right)^2-n-1\right)##
These examples mentioned above are very close to the solution but unfortunately wrong.
What I want...
Thank you very much for the very comprehensive response.
I need the recursive formula because I have to demonstrate with another program (mathlab) that at high sequnze of n (very high) the value tends to a value x.
To do this I cannot be satisfied with an approximation but rather with a...
I have been debating this issue for days:
I can't find a recursive function of this equation:
##\large{\sqrt{2+\pi \sqrt{3+\pi\sqrt{4+\pi\sqrt{5+\dotsb}}}}}##
Starting value 2 always added with pi
has been trying to find a solution this for days now, is what I have achieved so far:
This...