DLMF:23.6.E4 (Q7245): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12049 / rank
 
Normal rank
Property / Symbols used: Q12049 / qualifier
 
Defining formula:

ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}

\omega_{1}
Property / Symbols used: Q12049 / qualifier
 
xml-id: C23.S1.XMD8.m1cdec

Latest revision as of 15:46, 2 January 2020

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DLMF:23.6.E4
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    Statements

    Defining formula
    e 3 ⁡ = - π 2 12 ⁢ ω 1 2 ⁢ ( 2 ⁢ θ 2 4 ⁡ ( 0 , q ) + θ 4 4 ⁡ ( 0 , q ) ) . Weierstrass-e-on-lattice 3 𝕃 superscript 𝜋 2 12 superscript subscript 𝜔 1 2 2 Jacobi-theta 2 4 0 𝑞 Jacobi-theta 4 4 0 𝑞 {\displaystyle{\displaystyle e_{3}=-\frac{\pi^{2}}{12\omega_{1}^{2}}\left(2{% \theta_{2}^{4}}\left(0,q\right)+{\theta_{4}^{4}}\left(0,q\right)\right).}}
    0 references
    DLMF id
    DLMF:23.6.E4
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2abdec
    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.m2acdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1bdec
    0 references
    Q12066
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C23.S1.XMD10.m1cdec
    0 references
    Q12049
    Defining formula
    ω 1 subscript 𝜔 1 {\displaystyle{\displaystyle\omega_{1}}}
    xml-id
    C23.S1.XMD8.m1cdec
    0 references
     
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