Unit-interval representation at arbitrary Dirichlet parameters

theorem DirichletTransform.carlsonRUnitIntervalIntegral_eq_gamma_mul_continued {ι : Type u_1} [Fintype ι] {a a' : ℂ} {b z : ι → ℂ} (ha : 0 < a.re) (ha' : 0 < a'.re) (hsum : a + a' = ∑ i : ι, b i) (hz : z ∈ carlsonRVariableDomain) : carlsonRUnitIntervalIntegral a a' b z = Complex.Gamma a * Complex.Gamma a' * regCarlsonRContinued (-a) z hz b

Carlson's single-integral representation for arbitrary complex Dirichlet parameters. The restrictions concern only the convergent endpoint exponents, not the individual entries of b.