∀ {k : ℕ} {x : ℝ},
  k ≠ 0 →
    x ∈ Set.Icc 0 1 →
      HurwitzZeta.sinZeta (↑x) (2 * ↑k + 1) =
        (-1) ^ (k + 1) * (2 * ↑Real.pi) ^ (2 * k + 1) / 2 / ↑(2 * k + 1).factorial *
          Polynomial.eval (↑x) (Polynomial.map (algebraMap ℚ ℂ) (Polynomial.bernoulli (2 * k + 1)))