jacobiTheta₂''_conj — Mathlib

English

Jacobi theta function with the negated first argument satisfies jacobiTheta₂''(-z,τ) = - jacobiTheta₂''(z,τ).

Русский

Функция jacobiTheta₂''(−z,τ) равна −JacobiTheta₂''(z,τ).

LaTeX

$$$$\\operatorname{jacobiTheta_2''}(-z,\\tau) = -\\operatorname{jacobiTheta_2''}(z,\\tau).$$$$

Lean4

theorem jacobiTheta₂''_conj (z τ : ℂ) : conj (jacobiTheta₂'' z τ) = jacobiTheta₂'' (conj z) (-conj τ) := by
  simp [jacobiTheta₂'', jacobiTheta₂'_conj, jacobiTheta₂_conj, ← exp_conj, map_ofNat, div_neg, neg_div,
    jacobiTheta₂'_neg_left]

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