ウィルティンガーの微分
補題3.1 f , g ∈ C 1 ( Ω ) {\displaystyle f,g\in C^{1}(\Omega )} および g ( Ω ) ⊆ Ω {\displaystyle g(\Omega )\subseteq \Omega } であれば、チェインルールが成り立つ
∂ ∂ z ( f ∘ g ) = ( ∂ f ∂ z ∘ g ) ∂ g ∂ z + ( ∂ f ∂ z ̄ ∘ g ) ∂ g ̄ ∂ z {\displaystyle {\frac {\partial }{\partial z}}\left(f\circ g\right)=\left({\frac {\partial f}{\partial z}}\circ g\right){\frac {\partial g}{\partial z}}+\left({\frac {\partial f}{\partial {\bar {z}}}}\circ g\right){\frac {\partial {\bar {g}}}{\partial z}}}