DLMF:23.21.E5 (Q7387): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: DLMF:23.2.E4 / rank
 
Normal rank
Property / Symbols used: DLMF:23.2.E4 / qualifier
 
Defining formula:

℘ ⁡ ( z ) Weierstrass-P-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}

\Weierstrassplatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E4 / qualifier
 
xml-id: C23.S2.E4.m2aadec
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: Q12055 / rank
 
Normal rank
Property / Symbols used: Q12055 / qualifier
 
Defining formula:

𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}

\mathbb{L}
Property / Symbols used: Q12055 / qualifier
 
xml-id: C23.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12106 / rank
 
Normal rank
Property / Symbols used: Q12106 / qualifier
 
Defining formula:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q12106 / qualifier
 
xml-id: C23.S21.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q12107 / rank
 
Normal rank
Property / Symbols used: Q12107 / qualifier
 
Defining formula:

v 𝑣 {\displaystyle{\displaystyle v}}

v
Property / Symbols used: Q12107 / qualifier
 
xml-id: C23.S21.XMD7.m1adec
Property / Symbols used
 
Property / Symbols used: Q12108 / rank
 
Normal rank
Property / Symbols used: Q12108 / qualifier
 
Defining formula:

w 𝑤 {\displaystyle{\displaystyle w}}

w
Property / Symbols used: Q12108 / qualifier
 
xml-id: C23.S21.XMD8.m1adec

Latest revision as of 01:22, 2 January 2020

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English
DLMF:23.21.E5
No description defined

    Statements

    Defining formula
    ( ℘ ⁡ ( v ) - ℘ ⁡ ( w ) ) ⁢ ( ℘ ⁡ ( w ) - ℘ ⁡ ( u ) ) ⁢ ( ℘ ⁡ ( u ) - ℘ ⁡ ( v ) ) ⁢ ∇ 2 = ( ℘ ⁡ ( w ) - ℘ ⁡ ( v ) ) ⁢ ∂ 2 ∂ ⁡ u 2 + ( ℘ ⁡ ( u ) - ℘ ⁡ ( w ) ) ⁢ ∂ 2 ∂ ⁡ v 2 + ( ℘ ⁡ ( v ) - ℘ ⁡ ( u ) ) ⁢ ∂ 2 ∂ ⁡ w 2 . Weierstrass-P-on-lattice 𝑣 𝕃 Weierstrass-P-on-lattice 𝑤 𝕃 Weierstrass-P-on-lattice 𝑤 𝕃 Weierstrass-P-on-lattice 𝑢 𝕃 Weierstrass-P-on-lattice 𝑢 𝕃 Weierstrass-P-on-lattice 𝑣 𝕃 superscript ∇ 2 Weierstrass-P-on-lattice 𝑤 𝕃 Weierstrass-P-on-lattice 𝑣 𝕃 partial-derivative 𝑢 2 Weierstrass-P-on-lattice 𝑢 𝕃 Weierstrass-P-on-lattice 𝑤 𝕃 partial-derivative 𝑣 2 Weierstrass-P-on-lattice 𝑣 𝕃 Weierstrass-P-on-lattice 𝑢 𝕃 partial-derivative 𝑤 2 {\displaystyle{\displaystyle\left(\wp\left(v\right)-\wp\left(w\right)\right)% \left(\wp\left(w\right)-\wp\left(u\right)\right)\left(\wp\left(u\right)-\wp% \left(v\right)\right)\nabla^{2}=\left(\wp\left(w\right)-\wp\left(v\right)% \right)\frac{{\partial}^{2}}{{\partial u}^{2}}+\left(\wp\left(u\right)-\wp% \left(w\right)\right)\frac{{\partial}^{2}}{{\partial v}^{2}}+\left(\wp\left(v% \right)-\wp\left(u\right)\right)\frac{{\partial}^{2}}{{\partial w}^{2}}.}}
    0 references
    DLMF id
    DLMF:23.21.E5
    0 references
    Symbols used
    DLMF:23.2.E4
    Defining formula
    ℘ ⁡ ( z ) Weierstrass-P-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E4.m2aadec
    0 references
    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
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1cdec
    0 references
    Q12106
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C23.S21.XMD6.m1adec
    0 references
    Q12107
    Defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C23.S21.XMD7.m1adec
    0 references
    Q12108
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C23.S21.XMD8.m1adec
    0 references
     
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