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Formula:10671

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Digital Library of Mathematical Functions ID 36.10#Ex5

3 ⁢ ( ∂ 2 ⁡ Ψ ( E ) ∂ ⁡ x 2 - ∂ 2 ⁡ Ψ ( E ) ∂ ⁡ y 2 ) + 2 ⁢ i ⁢ z ⁢ ∂ ⁡ Ψ ( H ) ∂ ⁡ x - x ⁢ Ψ ( E ) = 0 . 3 partial-derivative elliptic-umbilic-canonical-integral 𝑥 2 partial-derivative elliptic-umbilic-canonical-integral 𝑦 2 2 𝑖 𝑧 partial-derivative hyperbolic-umbilic-canonical-integral 𝑥 𝑥 elliptic-umbilic-canonical-integral 0 {\displaystyle{\displaystyle 3\left(\frac{{\partial}^{2}\Psi^{(\mathrm{E})}}{{% \partial x}^{2}}-\frac{{\partial}^{2}\Psi^{(\mathrm{E})}}{{\partial y}^{2}}% \right)+2iz\frac{\partial\Psi^{(\mathrm{H})}}{\partial x}-x\Psi^{(\mathrm{E})}% =0.}}


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