Question:
I also noticed that you could get a closed form for a = 2. Do you have any
ideas what a would permit a similar thing to occur if instead of square
roots we take nth roots?

Replies:
Hey, that is a whole other can of worms! With nth roots you would have to
solve a n'th order polynomial equation to find the fixed point and it looks
like it gets an awful lot more complicated. My only idea is it is unlikely
there is a closed form for any n not equal to 2.

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