DLMF:20.5.E4 (Q6771): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11945 / rank
 
Normal rank
Property / Symbols used: Q11945 / qualifier
 
Defining formula:

θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}

\Jacobithetaq{\NVar{j}}@{\NVar{z}}{\NVar{q}}
Property / Symbols used: Q11945 / qualifier
 
xml-id: C20.S2.SS1.m2acdec

Revision as of 14:32, 2 January 2020

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DLMF:20.5.E4
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    Defining formula
    θ 4 ⁡ ( z , q ) = ∏ n = 1 ∞ ( 1 - q 2 ⁢ n ) ⁢ ( 1 - 2 ⁢ q 2 ⁢ n - 1 ⁢ cos ⁡ ( 2 ⁢ z ) + q 4 ⁢ n - 2 ) . Jacobi-theta 4 𝑧 𝑞 superscript subscript product 𝑛 1 1 superscript 𝑞 2 𝑛 1 2 superscript 𝑞 2 𝑛 1 2 𝑧 superscript 𝑞 4 𝑛 2 {\displaystyle{\displaystyle\theta_{4}\left(z,q\right)=\prod\limits_{n=1}^{% \infty}\left(1-q^{2n}\right)\left(1-2q^{2n-1}\cos\left(2z\right)+q^{4n-2}% \right).}}
    0 references
    DLMF id
    DLMF:20.5.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.m2acdec
    0 references
     
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