DLMF:20.7.E22 (Q6817)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:20.7.E22
No description defined

    Statements

    Defining formula
    θ 2 ⁡ ( 4 ⁢ z | 4 ⁢ τ ) = B ⁢ θ 2 ⁡ ( 1 8 ⁢ π - z | τ ) ⁢ θ 2 ⁡ ( 1 8 ⁢ π + z | τ ) ⁢ θ 2 ⁡ ( 3 8 ⁢ π - z | τ ) ⁢ θ 2 ⁡ ( 3 8 ⁢ π + z | τ ) , Jacobi-theta-tau 2 4 𝑧 4 𝜏 𝐵 Jacobi-theta-tau 2 1 8 𝜋 𝑧 𝜏 Jacobi-theta-tau 2 1 8 𝜋 𝑧 𝜏 Jacobi-theta-tau 2 3 8 𝜋 𝑧 𝜏 Jacobi-theta-tau 2 3 8 𝜋 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{2}\left(4z\middle|4\tau\right)=B\theta_{2}% \left(\tfrac{1}{8}\pi-z\middle|\tau\right)\theta_{2}\left(\tfrac{1}{8}\pi+z% \middle|\tau\right)\*\theta_{2}\left(\tfrac{3}{8}\pi-z\middle|\tau\right)% \theta_{2}\left(\tfrac{3}{8}\pi+z\middle|\tau\right),}}
    0 references
    DLMF id
    DLMF:20.7.E22
    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.m1agdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1rdec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1gdec
    0 references
    DLMF:20.7.E20
    Defining formula
    B 𝐵 {\displaystyle{\displaystyle B}}
    xml-id
    C20.S7.XMD2.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6817&oldid=49441"