hurwitzZetaOdd_eq — Mathlib

English

The Hurwitz zeta function satisfies the relation hurwitzZetaOdd a s = (hurwitzZeta a s − hurwitzZeta(−a) s)/2.

Русский

Функция Хёрвитц-зета удовлетворяет relation: hurwitzZetaOdd a s = (hurwitzZeta a s − hurwitzZeta(−a) s)/2.

LaTeX

$$$\mathrm{hurwitzZetaOdd}(a,s) = \dfrac{\mathrm{hurwitzZeta}(a,s) - \mathrm{hurwitzZeta}(-a,s)}{2}$$$

Lean4

theorem hurwitzZetaOdd_eq (a : UnitAddCircle) (s : ℂ) :
    hurwitzZetaOdd a s = (hurwitzZeta a s - hurwitzZeta (-a) s) / 2 :=
  by
  simp only [hurwitzZeta, hurwitzZetaEven_neg, hurwitzZetaOdd_neg]
  ring_nf

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