DLMF:1.9.E27 (Q302): 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.m4abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10813 / rank
 
Normal rank
Property / Symbols used: Q10813 / qualifier
 
Defining formula:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q10813 / qualifier
 
xml-id: C1.S9.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: Q10814 / rank
 
Normal rank
Property / Symbols used: Q10814 / qualifier
 
Defining formula:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q10814 / qualifier
 
xml-id: C1.S9.XMD2.m1fdec
Property / Symbols used
 
Property / Symbols used: Q10819 / rank
 
Normal rank
Property / Symbols used: Q10819 / qualifier
 
Defining formula:

u ⁢ ( x , y ) 𝑢 𝑥 𝑦 {\displaystyle{\displaystyle u(x,y)}}

u(x,y)
Property / Symbols used: Q10819 / qualifier
 
xml-id: C1.S9.XMD7.m1bdec

Latest revision as of 16:07, 1 January 2020

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DLMF:1.9.E27
No description defined

    Statements

    Defining formula
    ∂ 2 ⁡ u ∂ ⁡ r 2 + 1 r ⁢ ∂ ⁡ u ∂ ⁡ r + 1 r 2 ⁢ ∂ 2 ⁡ u ∂ ⁡ θ 2 = 0 partial-derivative 𝑢 𝑟 2 1 𝑟 partial-derivative 𝑢 𝑟 1 superscript 𝑟 2 partial-derivative 𝑢 𝜃 2 0 {\displaystyle{\displaystyle\frac{{\partial}^{2}u}{{\partial r}^{2}}+\frac{1}{% r}\frac{\partial u}{\partial r}+\frac{1}{r^{2}}\frac{{\partial}^{2}u}{{% \partial\theta}^{2}}=0}}
    0 references
    DLMF id
    DLMF:1.9.E27
    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.m4abdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2abdec
    0 references
    Q10813
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C1.S9.XMD1.m1ddec
    0 references
    Q10814
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C1.S9.XMD2.m1fdec
    0 references
    Q10819
    Defining formula
    u ⁢ ( x , y ) 𝑢 𝑥 𝑦 {\displaystyle{\displaystyle u(x,y)}}
    xml-id
    C1.S9.XMD7.m1bdec
    0 references
     
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