hasDerivAt_Gamma_one — Mathlib

English

For all n ∈ ℕ, HasDerivAt Gamma (n+1) equals n!(-γ + H_n) in the complex setting.

Русский

Для всех n ∈ ℕ HasDerivAt Γ (n+1) = n!(−γ + H_n) в комплексном контексте.

LaTeX

$$HasDerivAt Gamma (n ! * (-γ + H_n)) (n + 1)$$

Lean4

theorem hasDerivAt_Gamma_one : HasDerivAt Gamma (-γ) 1 := by
  simpa only [factorial_zero, cast_one, harmonic_zero, Rat.cast_zero, add_zero, mul_neg, one_mul, cast_zero,
    zero_add] using hasDerivAt_Gamma_nat 0

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