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DLMF:19.25.E41 - MaRDI portal

DLMF:19.25.E41 (Q7245)

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DLMF:19.25.E41
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    Statements

    DLMF defining formula
    σ j ⁢ ( z ) = exp ⁡ ( - η j ⁢ z ) ⁢ σ ⁡ ( z + ω j ) / σ ⁡ ( ω j ) , subscript 𝜎 𝑗 𝑧 subscript 𝜂 𝑗 𝑧 Weierstrass-sigma-on-lattice 𝑧 subscript 𝜔 𝑗 𝕃 Weierstrass-sigma-on-lattice subscript 𝜔 𝑗 𝕃 {\displaystyle{\displaystyle\sigma_{j}(z)=\exp\left(-\eta_{j}z\right)\sigma% \left(z+\omega_{j}\right)/\sigma\left(\omega_{j}\right),}}
    0 references
    constraint
    j = 1 , 2 , 3 𝑗 1 2 3 {\displaystyle{\displaystyle j=1,2,3}}
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    Symbols used
    23.2.E6
    DLMF defining formula
    σ ⁡ ( z ) Weierstrass-sigma-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\sigma\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E6.m2aadec
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    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    ( = 1 , 2 , 3 )
    DLMF defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C19.S25.XMD3.m1cdec
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    complex number
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C19.S25.XMD4.m1ddec
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    nonzero complex number
    DLMF defining formula
    ω j subscript 𝜔 𝑗 {\displaystyle{\displaystyle\omega_{j}}}
    xml-id
    C19.S25.XMD7.m1bdec
    0 references
    complex number
    DLMF defining formula
    η j subscript 𝜂 𝑗 {\displaystyle{\displaystyle\eta_{j}}}
    xml-id
    C19.S25.XMD8.m1adec
    0 references

    Identifiers

     
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