DLMF:23.2.E17 (Q7212): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12062 / rank
 
Normal rank
Property / Symbols used: Q12062 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12062 / qualifier
 
xml-id: C23.S6.XMD3.m1dec

Latest revision as of 15:43, 2 January 2020

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DLMF:23.2.E17
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    Statements

    Defining formula
    σ ⁡ ( z + 2 ⁢ m ⁢ ω j + 2 ⁢ n ⁢ ω k ) / σ ⁡ ( z ) = ( - 1 ) m + n + m ⁢ n ⁢ exp ⁡ ( ( 2 ⁢ m ⁢ η j + 2 ⁢ n ⁢ η k ) ⁢ ( m ⁢ ω j + n ⁢ ω k + z ) ) . Weierstrass-sigma-on-lattice 𝑧 2 𝑚 subscript 𝜔 𝑗 2 𝑛 subscript 𝜔 𝑘 𝕃 Weierstrass-sigma-on-lattice 𝑧 𝕃 superscript 1 𝑚 𝑛 𝑚 𝑛 2 𝑚 subscript 𝜂 𝑗 2 𝑛 subscript 𝜂 𝑘 𝑚 subscript 𝜔 𝑗 𝑛 subscript 𝜔 𝑘 𝑧 {\displaystyle{\displaystyle\ifrac{\sigma\left(z+2m\omega_{j}+2n\omega_{k}% \right)}{\sigma\left(z\right)}=(-1)^{m+n+mn}\exp\left((2m\eta_{j}+2n\eta_{k})(% m\omega_{j}+n\omega_{k}+z)\right).}}
    0 references
    DLMF id
    DLMF:23.2.E17
    0 references
    Symbols used
    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.m2addec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1kdec
    0 references
    Q12060
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C23.S1.XMD3.m1dec
    0 references
    Q12061
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C23.S1.XMD4.m1dec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1hdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1idec
    0 references
    Q12059
    Defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C23.S2.XMD6.m1fdec
    0 references
    Q12062
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C23.S6.XMD3.m1dec
    0 references
     
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