Complex.hasDerivAt_GammaIntegral

∀ {s : ℂ},
  0 < s.re →
    HasDerivAt Complex.GammaIntegral (∫ (t : ℝ) in Set.Ioi 0, ↑t ^ (s - 1) * (↑(Real.log t) * ↑(Real.exp (-t)))) s

The derivative of the Γ integral, at any s ∈ ℂ with 1 < re s, is given by the Mellin transform of log t * exp (-t).

Defined in: Mathlib.Analysis.SpecialFunctions.Gamma.Deriv
Cited by: 1 results in Mathlib
Foundations: Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.