cosKernel — Mathlib

English

If x ≤ 0, the cosKernel evaluates to 0.

Русский

Если x ≤ 0, cosKernel равен 0.

LaTeX

$$$$\\text{If } x \\le 0,\\quad \\cosKernel(a,x) = 0.$$$$

Lean4

/-- Cosine Hurwitz zeta kernel. See `cosKernel_def` for the defining formula, and
`hasSum_int_cosKernel` for expression as a sum. -/
@[irreducible]
def cosKernel (a : UnitAddCircle) (x : ℝ) : ℝ :=
  (show Function.Periodic (fun ξ : ℝ ↦ re (jacobiTheta₂ ξ (I * x))) 1 by intro ξ; simp [jacobiTheta₂_add_left]).lift a

Похожие утверждения