Multidimensional Theta Functions - 21.6 Products

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
21.6.E6	${\displaystyle{\displaystyle\theta\left(\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}\middle|\boldsymbol{{\Omega}}\right)=\frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}{\mathbb{Z}^{g}}/{\mathbb{Z}^{g}}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}{\mathbb{Z}^{g}}/{\mathbb{Z}^{g}}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\theta\left(\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right)}}$ \Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\frac{\mathbf{x}-\mathbf{y}-\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}} = \frac{1}{2^{g}}\sum_{\boldsymbol{{\alpha}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}\,\sum_{\boldsymbol{{\beta}}\in\frac{1}{2}\Integers^{g}/\Integers^{g}}e^{2\pi i\left(2\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}]\right)}\*\Riemanntheta@{\mathbf{x}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{y}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{u}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}\Riemanntheta@{\mathbf{v}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}}{\boldsymbol{{\Omega}}}		RiemannTheta((x + y + u + v)/(2), Omega)*RiemannTheta((x + y - u - v)/(2), Omega)*RiemannTheta((x - y + u - v)/(2), Omega)*RiemannTheta((x - y - u + v)/(2), Omega) = (1)/((2)^(g))*sum(sum(exp(2*Pi*I*(2*alpha * Omega * alpha + alpha *(x + y + u + v)))* RiemannTheta(x + Omega*alpha + beta, Omega)*RiemannTheta(y + Omega*alpha + beta, Omega)*RiemannTheta(u + Omega*alpha + beta, Omega)*RiemannTheta(v + Omega*alpha + beta, Omega), = ..infinity), = ..infinity)	Error	Missing Macro Error	Missing Macro Error	-	-