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We study nonlinear trident in laser pulses in the high-energy limit, wherethe initial electron experiences, in its rest frame, an electromagnetic fieldstrength above Schwinger's critical field. At lower energies the dominantcontribution comes from the "two-step" part, but in the high-energy limit thedominant contribution comes instead from the one-step term. We obtain newapproximations that explain the relation between the high-energy limit oftrident and pair production by a Coulomb field, as well as the role of theWeizs\"acker-Williams approximation and why it does not agree with thehigh-$\chi$ limit of the locally-constant-field approximation. We also showthat the next-to-leading order in the large-$a_0$ expansion is, in thehigh-energy limit, nonlocal and is numerically very important even for quitelarge $a_0$. We show that the small-$a_0$ perturbation series has a finiteradius of convergence, but using Pad\'e-conformal methods we obtainresummations that go beyond the radius of convergence and have a largenumerical overlap with the large-$a_0$ approximation. We useBorel-Pad\'e-conformal methods to resum the small-$\chi$ expansion and obtain ahigh precision up to very large $\chi$. We also use newer resummation methodsbased on hypergeometric/Meijer-G and confluent hypergeometric functions.

Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations