A Neighborhood of Infinity: Logarithms and exponentials of functions

An exploration of functional logarithms and exponentials for formal power series, enabling computation of fractional iterates of functions (e.g., the 'square root' of sin). The approach avoids the naive power-series-of-power-series method (which fails due to lack of distributivity) by using a clever operator that restores right-distributivity. The resulting `flog` and `fexp` functions are implemented in idiomatic lazy-list-based lazy evaluation in haskell, verified against known sequences in the oeis, and connected to differential geometry via flows and exponential maps.