∀ {ι : Type u_2} [inst : Fintype ι] {b : ι → ℂ},
  (∀ (i : ι), 0 < (b i).re) →
    ∀ (c : ι → ℂ),
      ∫ (v : ι → ℝ), Complex.exp (-∑ i, b i * ↑(v i) ^ 2 + ∑ i, c i * ↑(v i)) =
        ∏ i, (↑Real.pi / b i) ^ (1 / 2) * Complex.exp (c i ^ 2 / (4 * b i))