DLMF:28.32.E3 (Q8552)

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DLMF:28.32.E3
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    Statements

    test
    ∂ 2 ⁡ V ∂ ⁡ ξ 2 + ∂ 2 ⁡ V ∂ ⁡ η 2 + 1 2 ⁢ c 2 ⁢ k 2 ⁢ ( cosh ⁡ ( 2 ⁢ ξ ) - cos ⁡ ( 2 ⁢ η ) ) ⁢ V = 0 . partial-derivative 𝑉 𝜉 2 partial-derivative 𝑉 𝜂 2 1 2 superscript 𝑐 2 superscript 𝑘 2 2 𝜉 2 𝜂 𝑉 0 {\displaystyle{\displaystyle\frac{{\partial}^{2}V}{{\partial\xi}^{2}}+\frac{{% \partial}^{2}V}{{\partial\eta}^{2}}+\frac{1}{2}c^{2}k^{2}(\cosh\left(2\xi% \right)-\cos\left(2\eta\right))V=0.}}
    0 references
    DLMF id
    DLMF:28.32.E3
    0 references
    Symbols used
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    hyperbolic cosine function
    test
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aadec
    0 references
    partial derivative of $$f$$ with respect to $$x$$
    test
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4aadec
    0 references
    partial differential of $$x$$
    test
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q12333
    test
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C28.S32.XMD1.m1adec
    0 references
    Q12334
    test
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C28.S32.XMD2.m1adec
    0 references
    Q12331
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C28.S32.XMD3.m1adec
    0 references
    Q12332
    test
    V ⁢ ( ξ , η ) 𝑉 𝜉 𝜂 {\displaystyle{\displaystyle V(\xi,\eta)}}
    xml-id
    C28.S32.XMD4.m1adec
    0 references
     
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