Formula:9609

Digital Library of Mathematical Functions ID 30.13.E4

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle h_{\eta}^{2}=\left(\pderiv{x}{\eta}\right)^{2}+\left(\pderiv{y}{\eta}\right)^{2}+\left(\pderiv{z}{\eta}\right)^{2}=\frac{c^{2}(\xi^{2}-\eta^{2})}{1-\eta^{2}},}

Symbols List

• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle\xi}}$: prolate spheroidal coordinate
• ${\displaystyle{\displaystyle\eta}}$: prolate spheroidal coordinate
• ${\displaystyle{\displaystyle c}}$: positive constant
• ${\displaystyle{\displaystyle h_{\xi},h_{\eta},h_{\phi}}}$: metric coefficients
 

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