DLMF:20.6.E4 (Q6788)

From DRMF
Revision as of 14:36, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:20.6.E4
No description defined

    Statements

    Defining formula
    θ 3 ⁡ ( π ⁢ z | τ ) = θ 3 ⁡ ( 0 | τ ) ⁢ exp ⁡ ( - ∑ j = 1 ∞ 1 2 ⁢ j ⁢ β 2 ⁢ j ⁢ ( τ ) ⁢ z 2 ⁢ j ) , Jacobi-theta-tau 3 𝜋 𝑧 𝜏 Jacobi-theta-tau 3 0 𝜏 superscript subscript 𝑗 1 1 2 𝑗 subscript 𝛽 2 𝑗 𝜏 superscript 𝑧 2 𝑗 {\displaystyle{\displaystyle\theta_{3}\left(\pi z\middle|\tau\right)=\theta_{3% }\left(0\middle|\tau\right)\exp\left(-\sum_{j=1}^{\infty}\frac{1}{2j}\beta_{2j% }(\tau)z^{2j}\right),}}
    0 references
    DLMF id
    DLMF:20.6.E4
    0 references
    Symbols used
    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6788&oldid=48853"