DLMF:23.10.E3 (Q7301): 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: DLMF:23.2.E6 / rank
 
Normal rank
Property / Symbols used: DLMF:23.2.E6 / qualifier
 
Defining formula:

σ ⁡ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}

\Weierstrasssigmalatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E6 / qualifier
 
xml-id: C23.S2.E6.m2adec
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.m1bdec

Latest revision as of 15:58, 2 January 2020

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DLMF:23.10.E3
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    Statements

    Defining formula
    σ ⁡ ( u + v ) ⁢ σ ⁡ ( u - v ) σ 2 ⁡ ( u ) ⁢ σ 2 ⁡ ( v ) = ℘ ⁡ ( v ) - ℘ ⁡ ( u ) , Weierstrass-sigma-on-lattice 𝑢 𝑣 𝕃 Weierstrass-sigma-on-lattice 𝑢 𝑣 𝕃 Weierstrass-sigma-on-lattice 2 𝑢 𝕃 Weierstrass-sigma-on-lattice 2 𝑣 𝕃 Weierstrass-P-on-lattice 𝑣 𝕃 Weierstrass-P-on-lattice 𝑢 𝕃 {\displaystyle{\displaystyle\frac{\sigma\left(u+v\right)\sigma\left(u-v\right)% }{{\sigma^{2}}\left(u\right){\sigma^{2}}\left(v\right)}=\wp\left(v\right)-\wp% \left(u\right),}}
    0 references
    DLMF id
    DLMF:23.10.E3
    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
    DLMF:23.2.E6
    Defining formula
    σ ⁡ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E6.m2adec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1bdec
    0 references
     
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