DLMF:21.5.E4 (Q6881)

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Language	Label	Description	Also known as
English	DLMF:21.5.E4	No description defined

Statements

Defining formula

{\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).}}

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DLMF:21.5.E4

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Riemann theta function

Defining formula

{\displaystyle{\displaystyle\theta\left(\NVar{\mathbf{z}}\middle|\NVar{% \boldsymbol{{\Omega}}}\right)}}

C21.S2.E1.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\det}}

C1.S3.SS1.m1aadec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}

C21.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle\boldsymbol{{\Gamma}}}}

C21.S5.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle\xi(\boldsymbol{{\Gamma}})}}

C21.S5.XMD2.m1dec

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Sitelinks

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