DLMF:23.5.E7 (Q7236)

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DLMF:23.5.E7
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    Statements

    Defining formula
    e 1 ⁡ = e 2 ⁢ π ⁢ i / 3 ⁢ e 3 ⁡ = e - 2 ⁢ π ⁢ i / 3 ⁢ e 2 ⁡ = ( Γ ⁡ ( 1 3 ) ) 6 2 14 / 3 ⁢ π 2 ⁢ ω 1 2 , Weierstrass-e-on-lattice 1 𝕃 superscript 𝑒 2 𝜋 𝑖 3 Weierstrass-e-on-lattice 3 𝕃 superscript 𝑒 2 𝜋 𝑖 3 Weierstrass-e-on-lattice 2 𝕃 superscript Euler-Gamma 1 3 6 superscript 2 14 3 superscript 𝜋 2 superscript subscript 𝜔 1 2 {\displaystyle{\displaystyle e_{1}=e^{2\pi i/3}e_{3}=e^{-2\pi i/3}e_{2}=\frac{% \left(\Gamma\left(\tfrac{1}{3}\right)\right)^{6}}{2^{14/3}\pi^{2}\omega_{1}^{2% }},}}
    0 references
    DLMF id
    DLMF:23.5.E7
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    Q11869
    Defining formula
    e j ⁡ Weierstrass-e-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle e_{\NVar{j}}}}
    xml-id
    C23.S3.SS1.m1abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1cdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1fdec
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