Theorems · Theorem · commutative algebra

PowerSeries.exp_mul_exp_eq_exp_add

∀ {A : Type u_4} [inst : CommRing A] [inst_1 : Algebra ℚ A] (a b : A),
  (PowerSeries.rescale a) (PowerSeries.exp A) * (PowerSeries.rescale b) (PowerSeries.exp A) =
    (PowerSeries.rescale (a + b)) (PowerSeries.exp A)

Shows that $e^{aX} * e^{bX} = e^{(a + b)X}$

Defined in

Mathlib.RingTheory.PowerSeries.Exp

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAlgebra