Using complex analysis to study generating functions that describe time complexity is definitely interesting, and there are some cases where using generating fu

Using complex analysis to study generating functions that describe time complexity is definitely interesting, and there are some cases where using generating functions can make a complicated analysis a bit easier to deal with, but I don't see any reason to think that analytic combinatorics is more practical on a day-to-day basis than big-O notation. Analytic combinatorics is much closer in spirit to the techniques that Knuth uses to analyze performance in The Art of Computer Programming, and I don't know many programmers who prefer Knuth's style of analysis to big-O.