Formula:7576

Digital Library of Mathematical Functions ID 21.5.E4

${\displaystyle{\displaystyle\theta\left(\left[[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\right]^{\mathrm{T}}\mathbf{z}\middle|[\mathbf{A}\boldsymbol{{\Omega}}+\mathbf{B}][\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\right)=\xi(\boldsymbol{{\Gamma}})\sqrt{\det[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]}e^{\pi i\mathbf{z}\cdot\left[[\mathbf{C}\boldsymbol{{\Omega}}+\mathbf{D}]^{-1}\mathbf{C}\right]\cdot\mathbf{z}}\theta\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{\boldsymbol{{\Omega}}}\right)}}$: Riemann theta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\det}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$: a Riemann matrix
• ${\displaystyle{\displaystyle\boldsymbol{{\Gamma}}}}$: 21.5.E1
• ${\displaystyle{\displaystyle\xi(\boldsymbol{{\Gamma}})}}$: eighth root of unity
 

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