Differentiation of the entire Carlson S-function

theorem DirichletTransform.carlsonPartialDeriv_regCarlsonSSeries {ι : Type u_1} [Fintype ι] (i : ι) (z b : ι → ℂ) : carlsonPartialDeriv i (fun (z : ι → ℂ) => regCarlsonSSeries z b) z = b i * regCarlsonSSeries z (addDirichletUnit b i)

Carlson's differentiation formula for the analytically continued S function.