Formula:7602

Digital Library of Mathematical Functions ID 21.7.E10

${\displaystyle{\displaystyle\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{3}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z}+\int_{P_{2}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)E(P_{3},P_{2})E(P_{1},P_{4})+\theta\left(\mathbf{z}+\int_{P_{2}}^{P_{3}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)E(P_{3},P_{1})E(P_{4},P_{2})=\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)\theta\left(\mathbf{z}+\int_{P_{1}}^{P_{3}}\boldsymbol{{\omega}}+\int_{P_{2}}^{P_{4}}\boldsymbol{{\omega}}\middle|\boldsymbol{{\Omega}}\right)E(P_{1},P_{2})E(P_{3},P_{4}),}}$

Symbols List

• ${\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$: Riemann theta function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
• ${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$: a Riemann matrix
• ${\displaystyle{\displaystyle E(P_{1},P_{2})}}$: prime form (locally)
• ${\displaystyle{\displaystyle P_{1},P_{2}}}$: points
• ${\displaystyle{\displaystyle\boldsymbol{{\omega}}}}$: vector of differentials
 

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