DLMF:31.10.E18 (Q9071): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12501 / rank
 
Normal rank
Property / Symbols used: Q12501 / qualifier
 
Defining formula:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q12501 / qualifier
 
xml-id: C31.S10.XMD15.m1adec
Property / Symbols used
 
Property / Symbols used: Q12499 / rank
 
Normal rank
Property / Symbols used: Q12499 / qualifier
 
Defining formula:

w 𝑤 {\displaystyle{\displaystyle w}}

w
Property / Symbols used: Q12499 / qualifier
 
xml-id: C31.S10.XMD16.m1ddec

Latest revision as of 13:38, 2 January 2020

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DLMF:31.10.E18
No description defined

    Statements

    Defining formula
    ∂ 2 ⁡ 𝒦 ∂ ⁡ u 2 + ∂ 2 ⁡ 𝒦 ∂ ⁡ v 2 + ∂ 2 ⁡ 𝒦 ∂ ⁡ w 2 + 2 ⁢ γ - 1 u ⁢ ∂ ⁡ 𝒦 ∂ ⁡ u + 2 ⁢ δ - 1 v ⁢ ∂ ⁡ 𝒦 ∂ ⁡ v + 2 ⁢ ϵ - 1 w ⁢ ∂ ⁡ 𝒦 ∂ ⁡ w = 0 . partial-derivative 𝒦 𝑢 2 partial-derivative 𝒦 𝑣 2 partial-derivative 𝒦 𝑤 2 2 𝛾 1 𝑢 partial-derivative 𝒦 𝑢 2 𝛿 1 𝑣 partial-derivative 𝒦 𝑣 2 italic-ϵ 1 𝑤 partial-derivative 𝒦 𝑤 0 {\displaystyle{\displaystyle\frac{{\partial}^{2}\mathcal{K}}{{\partial u}^{2}}% +\frac{{\partial}^{2}\mathcal{K}}{{\partial v}^{2}}+\frac{{\partial}^{2}% \mathcal{K}}{{\partial w}^{2}}+\frac{2\gamma-1}{u}\frac{\partial\mathcal{K}}{% \partial u}+\frac{2\delta-1}{v}\frac{\partial\mathcal{K}}{\partial v}+\frac{2% \epsilon-1}{w}\frac{\partial\mathcal{K}}{\partial w}=0.}}
    0 references
    DLMF id
    DLMF:31.10.E18
    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.m4aedec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aedec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1hdec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1hdec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1hdec
    0 references
    kernel (locally)
    Defining formula
    𝒦 ⁢ ( z ; s , t ) 𝒦 𝑧 𝑠 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z;s,t)}}
    xml-id
    C31.S10.XMD13.m1ddec
    0 references
    Q12500
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C31.S10.XMD14.m1adec
    0 references
    Q12501
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C31.S10.XMD15.m1adec
    0 references
    Q12499
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C31.S10.XMD16.m1ddec
    0 references
     
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