DLMF:12.17.E4 (Q4287): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

\pderiv{\NVar{f}}{\NVar{x}}
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S5.E3.m4aadec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11553 / rank
 
Normal rank
Property / Symbols used: Q11553 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11553 / qualifier
 
xml-id: C12.S17.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11554 / rank
 
Normal rank
Property / Symbols used: Q11554 / qualifier
 
Defining formula:

ξ 𝜉 {\displaystyle{\displaystyle\xi}}

\xi
Property / Symbols used: Q11554 / qualifier
 
xml-id: C12.S17.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11555 / rank
 
Normal rank
Property / Symbols used: Q11555 / qualifier
 
Defining formula:

η 𝜂 {\displaystyle{\displaystyle\eta}}

\eta
Property / Symbols used: Q11555 / qualifier
 
xml-id: C12.S17.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11556 / rank
 
Normal rank
Property / Symbols used: Q11556 / qualifier
 
Defining formula:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: Q11556 / qualifier
 
xml-id: C12.S17.XMD4.m1adec

Latest revision as of 15:34, 2 January 2020

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DLMF:12.17.E4
No description defined

    Statements

    Defining formula
    1 ξ 2 + η 2 ⁢ ( ∂ 2 ⁡ w ∂ ⁡ ξ 2 + ∂ 2 ⁡ w ∂ ⁡ η 2 ) + ∂ 2 ⁡ w ∂ ⁡ ζ 2 + k 2 ⁢ w = 0 . 1 superscript 𝜉 2 superscript 𝜂 2 partial-derivative 𝑤 𝜉 2 partial-derivative 𝑤 𝜂 2 partial-derivative 𝑤 𝜁 2 superscript 𝑘 2 𝑤 0 {\displaystyle{\displaystyle\frac{1}{\xi^{2}+\eta^{2}}\left(\frac{{\partial}^{% 2}w}{{\partial\xi}^{2}}+\frac{{\partial}^{2}w}{{\partial\eta}^{2}}\right)+% \frac{{\partial}^{2}w}{{\partial\zeta}^{2}}+k^{2}w=0.}}
    0 references
    DLMF id
    DLMF:12.17.E4
    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.m4aadec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2aadec
    0 references
    Q11553
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C12.S17.XMD1.m1adec
    0 references
    Q11554
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C12.S17.XMD2.m1adec
    0 references
    Q11555
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C12.S17.XMD3.m1adec
    0 references
    Q11556
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C12.S17.XMD4.m1adec
    0 references
     
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