Complex.integral_cpow_mul_exp_neg_mul_Ioi

∀ {a : ℂ} {r : ℝ},
  0 < a.re → 0 < r → ∫ (t : ℝ) in Set.Ioi 0, ↑t ^ (a - 1) * Complex.exp (-(↑r * ↑t)) = (1 / ↑r) ^ a * Complex.Gamma a

Expresses the integral over Ioi 0 of t ^ (a - 1) * exp (-(r * t)) in terms of the Gamma function, for complex a.

Defined in: Mathlib.Analysis.SpecialFunctions.Gamma.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound

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