DLMF:30.13.E3 (Q8916)

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DLMF:30.13.E3
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    Statements

    Defining formula
    h ξ 2 = ( ∂ ⁡ x ∂ ⁡ ξ ) 2 + ( ∂ ⁡ y ∂ ⁡ ξ ) 2 + ( ∂ ⁡ z ∂ ⁡ ξ ) 2 = c 2 ⁢ ( ξ 2 - η 2 ) ξ 2 - 1 , superscript subscript ℎ 𝜉 2 superscript partial-derivative 𝑥 𝜉 2 superscript partial-derivative 𝑦 𝜉 2 superscript partial-derivative 𝑧 𝜉 2 superscript 𝑐 2 superscript 𝜉 2 superscript 𝜂 2 superscript 𝜉 2 1 {\displaystyle{\displaystyle h_{\xi}^{2}=\left(\frac{\partial x}{\partial\xi}% \right)^{2}+\left(\frac{\partial y}{\partial\xi}\right)^{2}+\left(\frac{% \partial z}{\partial\xi}\right)^{2}=\frac{c^{2}(\xi^{2}-\eta^{2})}{\xi^{2}-1},}}
    0 references
    DLMF id
    DLMF:30.13.E3
    0 references
    Symbols used
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
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    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q12401
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C30.S1.XMD1.m1adec
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    Q12419
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C30.S1.XMD2.m1adec
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    Q12435
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C30.S1.XMD3.m1adec
    0 references
    Q12436
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C30.S13.XMD1.m1bdec
    0 references
    Q12437
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C30.S13.XMD2.m1bdec
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    Q12438
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C30.S13.XMD4.m1adec
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    Q12439
    Defining formula
    h ξ , h η , h ϕ subscript ℎ 𝜉 subscript ℎ 𝜂 subscript ℎ italic-ϕ {\displaystyle{\displaystyle h_{\xi},h_{\eta},h_{\phi}}}
    xml-id
    C30.S13.XMD5.m1dec
    0 references
     
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