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fractional iterations
The notion of a fractional iteration of a function was one of my obsessions when I was in high school... but there was no Wikipedia or Google back then, so I never knew about the work that existed.
reference list on Iterative Roots and Fractional Iteration
reference list on Iterative Roots and Fractional Iteration
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tangential: while trying to write this reply I couldn't remember the name of the constant (kept googling "Franzen"), and came across a list of constants sorted by continued fraction representation