DLMF:23.12.E3 (Q7325)

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DLMF:23.12.E3
No description defined

    Statements

    Defining formula
    σ ⁡ ( z ) = 2 ⁢ ω 1 π ⁢ exp ⁡ ( π 2 ⁢ z 2 24 ⁢ ω 1 2 ) ⁢ sin ⁡ ( π ⁢ z 2 ⁢ ω 1 ) ⁢ ( 1 - ( π 2 ⁢ z 2 ω 1 2 - 4 ⁢ sin 2 ⁡ ( π ⁢ z 2 ⁢ ω 1 ) ) ⁢ q 2 + O ⁡ ( q 4 ) ) , Weierstrass-sigma-on-lattice 𝑧 𝕃 2 subscript 𝜔 1 𝜋 superscript 𝜋 2 superscript 𝑧 2 24 superscript subscript 𝜔 1 2 𝜋 𝑧 2 subscript 𝜔 1 1 superscript 𝜋 2 superscript 𝑧 2 superscript subscript 𝜔 1 2 4 2 𝜋 𝑧 2 subscript 𝜔 1 superscript 𝑞 2 Big-O superscript 𝑞 4 {\displaystyle{\displaystyle\sigma\left(z\right)=\frac{2\omega_{1}}{\pi}\exp% \left(\frac{\pi^{2}z^{2}}{24\omega_{1}^{2}}\right)\sin\left(\frac{\pi z}{2% \omega_{1}}\right)\*\left(1-\left(\frac{\pi^{2}z^{2}}{\omega_{1}^{2}}-4{\sin^{% 2}}\left(\frac{\pi z}{2\omega_{1}}\right)\right)q^{2}+O\left(q^{4}\right)% \right),}}
    0 references
    DLMF id
    DLMF:23.12.E3
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
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    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
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1bdec
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    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1bdec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1bdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1bdec
    0 references
     
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