∀ {𝕂 : Type u} [inst : Field 𝕂] [inst_1 : CharZero 𝕂] {𝔸 : Type v} [inst_2 : Ring 𝔸] [inst_3 : Algebra 𝕂 𝔸]
  [inst_4 : TopologicalSpace 𝔸] [inst_5 : IsTopologicalRing 𝔸] {a b : 𝕂},
  (∀ (k : ℕ), ↑k ≠ -b) →
    binomialSeries 𝔸 a = (ordinaryHypergeometricSeries 𝔸 (-a) b b).compContinuousLinearMap (-ContinuousLinearMap.id 𝕂 𝔸)