completedHurwitzZetaOdd — Mathlib

English

The odd part is odd in the first variable: completedHurwitzZetaOdd(-a, s) = - completedHurwitzZetaOdd(a, s).

Русский

Нечетная часть по первой переменной: completedHurwitzZetaOdd(-a, s) = - completedHurwitzZetaOdd(a, s).

LaTeX

$$$$ \, completedHurwitzZetaOdd(-a, s) = -\, completedHurwitzZetaOdd(a, s). $$$$

Lean4

/-- The entire function of `s` which agrees with
`1 / 2 * Gamma ((s + 1) / 2) * π ^ (-(s + 1) / 2) * ∑' (n : ℤ), sgn (n + a) / |n + a| ^ s`
for `1 < re s`.
-/
def completedHurwitzZetaOdd (a : UnitAddCircle) (s : ℂ) : ℂ :=
  ((hurwitzOddFEPair a).Λ ((s + 1) / 2)) / 2

Похожие утверждения