You find a lot of information in: Dmitri Alekseevky, Andreas Kriegl, Mark Losik, Peter W. Michor: Choosing roots of polynomials smoothly, Israel J. Math 105 (1998), p. 203-233. (pdf), and in related later papers. The formula that you seek (or the inverse) is on page 7.
added 178 characters in body; added 1 characters in body; deleted 179 characters in body; added 57 characters in body
Peter Michor
- 25.3k
- 2
- 64
- 112