Now, if the scalar value functions P u and P v are defined as follows, P u ( u , v ) = ( F ( ψ ψ ( u , v ) ) ⋅ ⋅ ∂ ∂ ψ ψ ∂ ∂ u ( u , v ) ) P v ( u , v ) = ( F ( ψ ψ ( u , v ) ) ⋅ ⋅ ∂ ∂ ψ ψ ∂ ∂ v ( u , v ) ) then, P ( u , v ) = P u ( u , v ) e u + P v ( u , v ) e v .