integral_gaussian_sq_complex

∀ {b : ℂ}, 0 < b.re → (∫ (x : ℝ), Complex.exp (-b * ↑x ^ 2)) ^ 2 = ↑Real.pi / b

The square of the Gaussian integral ∫ x:ℝ, exp (-b * x^2) is equal to π / b.

Defined in: Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral
Cited by: 2 results in Mathlib
Foundations: Depth 288 from the axioms · uses propext, Classical.choice, Quot.sound

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