5 ms·

Écalle's own summary can be found here: https://www.imo.universite-paris-saclay.fr/~jean.ecalle/fichiersweb/WEB_tour_resur.pdf https://www.imo.universite-paris-

• JPLeRouzic 4y ago
  I am not a scientist, is this Alien calculus akin (somehow) to a derivative?
  • pvitz 4y ago
    The capital delta acts like a "normal" derivative if you want to say so. In eq. 4, you can see the product rule which is one of the most defining features for any sort of calculus. However, I must admit that this summary will take me a lot of time to digest...
    • mcabbott 4y ago
      Yes, it obeys enough algebraic laws that calling it a derivative is useful. But I don't think there's any underlying notion of small changes to something continuous. It is not the slope of some smooth function.
  • scythe 4y ago
    It involves defining a set of operators — like functors in CS, operators take one function and return another — which obey a modified form of the product rule for derivatives D[f*g] = g*Df + f*Dg. These operators are used to make the analytic continuation of divergent series consistent; because they are defined in terms of functions that cannot be calculated directly from their definition (hence analytically continued), they are "alien".
• ajkjk 4y ago
  Man, I know a good bit of graduate-level math well and that is incomprehensible to me. Either it's very poorly written or it's targeted at an audience who are already experts in, specifically, Borel transforms and I guess functional analysis?