WA is unable to figure this out and have not found any resource on it. Maybe someone could come up with a method using integrals or differential equations.
How would one go about solving a recursion relation such as:
a(n+1)=A*a(n)^B/(C+a(n)) ?
If a particular value is required, let a(0)=1/2
For unknowns A,B,C that query seems out of reach of WolframAlpha.
WolframAlpha is able to provide some results for queries like this
RSolve[{a[n]==2*a[n-1]^3/(4+a[n-1]),a[0]==1/2},a[n],n]
That might help you get started, but that result may not be in the form that you desire
No doubt. That’s why I used specific numbers for Wolfram|Alpha. I wouldn’t expect it to solve it otherwise, of course. So my question still stands. Since Wolfram|Alpha is unable to do it, does anyone have a way they think would work?
Try for example,
a(n+1)=3 a(n)^(1/2)/(2+a(n)), a(0)=1/2