continuousAt_jacobiTheta — Mathlib

English

Jacobi theta is continuous in the upper half-plane; in particular, it is continuous at every point τ with Im(τ) > 0.

Русский

Функция θ непрерывна в верхней полуплоскости; в частности, непрерывна в любой точке τ с Im(τ) > 0.

LaTeX

$$$\text{ContinuousAt}(\jacobiTheta, \tau)\quad \text{for } \Im(\tau) > 0$$$

Lean4

theorem continuousAt_jacobiTheta {τ : ℂ} (hτ : 0 < im τ) : ContinuousAt jacobiTheta τ :=
  (differentiableAt_jacobiTheta hτ).continuousAt

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