DLMF:20.11.E5 (Q6846)

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DLMF:20.11.E5
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    Statements

    Defining formula
    F 1 2 ⁡ ( 1 2 , 1 2 ; 1 ; k 2 ) = θ 3 2 ⁡ ( 0 | τ ) ; Gauss-hypergeometric-F-as-2F1 1 2 1 2 1 superscript 𝑘 2 Jacobi-theta-tau 3 2 0 𝜏 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\tfrac{1}{2},\tfrac{1}{2};1;k^{% 2}\right)={\theta_{3}^{2}}\left(0\middle|\tau\right);}}
    0 references
    DLMF id
    DLMF:20.11.E5
    0 references
    Symbols used
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5adec
    0 references
    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.m1aadec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1adec
    0 references
     
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