calc
  _ = cexp (↑(Real.log x) * ((↑σ' - 1) + ↑t * I)) * (↑σ' + ↑t * I - 1)⁻¹ := by rw [← div_neg]; ring_nf
  _ = (x ^ ((↑σ' - 1) + ↑t * I)) * (↑σ' + ↑t * I - 1)⁻¹ := by
    rw [Complex.cpow_def_of_ne_zero (ofReal_ne_zero.mpr (ne_of_gt hx)), Complex.ofReal_log hx.le]
  _ = (x ^ ((σ' : ℂ) - 1)) * (x ^ (↑t * I)) * (↑σ' + ↑t * I - 1)⁻¹ := by
    rw [Complex.cpow_add _ _ (ofReal_ne_zero.mpr (ne_of_gt hx))]
  _ = _ := by rw [ofReal_cpow hx.le]; push_cast; ring
n : ℕ
A a b c d u x y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝ : _root_.RCLike 𝕜
hx : 0 < x
⊢ -(cexp (-((1 - ↑σ' - ↑t * I) * ↑x.log)) / (1 - ↑σ' - ↑t * I)) = ↑(x ^ (σ' - 1)) * (↑σ' + ↑t * I - 1)⁻¹ * ↑x ^ (↑t * I)
no goals