DLMF:14.30.E10 (Q4972)

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DLMF:14.30.E10
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    Statements

    Defining formula
    1 ρ 2 ⁢ ∂ ∂ ⁡ ρ ⁡ ( ρ 2 ⁢ ∂ ⁡ W ∂ ⁡ ρ ) + 1 ρ 2 ⁢ sin ⁡ θ ⁢ ∂ ∂ ⁡ θ ⁡ ( sin ⁡ θ ⁢ ∂ ⁡ W ∂ ⁡ θ ) + 1 ρ 2 ⁢ sin 2 ⁡ θ ⁢ ∂ 2 ⁡ W ∂ ⁡ ϕ 2 = 0 , 1 superscript 𝜌 2 partial-derivative 𝜌 superscript 𝜌 2 partial-derivative 𝑊 𝜌 1 superscript 𝜌 2 𝜃 partial-derivative 𝜃 𝜃 partial-derivative 𝑊 𝜃 1 superscript 𝜌 2 2 𝜃 partial-derivative 𝑊 italic-ϕ 2 0 {\displaystyle{\displaystyle{\frac{1}{\rho^{2}}\frac{\partial}{\partial\rho}% \left(\rho^{2}\frac{\partial W}{\partial\rho}\right)+\frac{1}{\rho^{2}\sin% \theta}\frac{\partial}{\partial\theta}\left(\sin\theta\frac{\partial W}{% \partial\theta}\right)}+\frac{1}{\rho^{2}{\sin^{2}}\theta}\frac{{\partial}^{2}% W}{{\partial\phi}^{2}}=0,}}
    0 references
    DLMF id
    DLMF:14.30.E10
    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
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
    0 references
    Q11643
    Defining formula
    W ⁢ ( ρ , θ , ϕ ) 𝑊 𝜌 𝜃 italic-ϕ {\displaystyle{\displaystyle W(\rho,\theta,\phi)}}
    xml-id
    C14.S30.XMD3.m1dec
    0 references
     
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