DLMF:20.7.E14 (Q6809)

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DLMF:20.7.E14
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    Statements

    Defining formula
    θ 3 ⁡ ( z , q ) ⁢ θ 3 ⁡ ( w , q ) = θ 3 ⁡ ( z + w , q 2 ) ⁢ θ 3 ⁡ ( z - w , q 2 ) + θ 2 ⁡ ( z + w , q 2 ) ⁢ θ 2 ⁡ ( z - w , q 2 ) . Jacobi-theta 3 𝑧 𝑞 Jacobi-theta 3 𝑤 𝑞 Jacobi-theta 3 𝑧 𝑤 superscript 𝑞 2 Jacobi-theta 3 𝑧 𝑤 superscript 𝑞 2 Jacobi-theta 2 𝑧 𝑤 superscript 𝑞 2 Jacobi-theta 2 𝑧 𝑤 superscript 𝑞 2 {\displaystyle{\displaystyle\theta_{3}\left(z,q\right)\theta_{3}\left(w,q% \right)=\theta_{3}\left(z+w,q^{2}\right)\theta_{3}\left(z-w,q^{2}\right)+% \theta_{2}\left(z+w,q^{2}\right)\theta_{2}\left(z-w,q^{2}\right).}}
    0 references
    DLMF id
    DLMF:20.7.E14
    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.m2amdec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1ldec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1mdec
    0 references
     
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