DLMF:21.6.E7 (Q6895)

No description defined

Language	Label	Description	Also known as
English	DLMF:21.6.E7	No description defined

Statements

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}+\mathbf{c}_{2}+\mathbf{c}_{3}+\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}+\mathbf{d}_{2}+\mathbf{d}_{3}+\mathbf{d}_{4}]}@{\frac{\mathbf{x}+\mathbf{y}+\mathbf{u}+\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}+\mathbf{c}_{2}-\mathbf{c}_{3}-\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}+\mathbf{d}_{2}-\mathbf{d}_{3}-\mathbf{d}_{4}]}@{\frac{\mathbf{x}+\mathbf{y}-\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\*\Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}-\mathbf{c}_{2}+\mathbf{c}_{3}-\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}-\mathbf{d}_{2}+\mathbf{d}_{3}-\mathbf{d}_{4}]}@{\frac{\mathbf{x}-\mathbf{y}+\mathbf{u}-\mathbf{v}}{2}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\tfrac{1}{2}[\mathbf{c}_{1}-\mathbf{c}_{2}-\mathbf{c}_{3}+\mathbf{c}_{4}]}{\tfrac{1}{2}[\mathbf{d}_{1}-\mathbf{d}_{2}-\mathbf{d}_{3}+\mathbf{d}_{4}]}@{\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\boldsymbol{{\beta}}\cdot[\mathbf{c}_{1}+\mathbf{c}_{2}+\mathbf{c}_{3}+\mathbf{c}_{4}]}\*\Riemannthetachar{\mathbf{c}_{1}+\boldsymbol{{\alpha}}}{\mathbf{d}_{1}+\boldsymbol{{\beta}}}@{\mathbf{x}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\mathbf{c}_{2}+\boldsymbol{{\alpha}}}{\mathbf{d}_{2}+\boldsymbol{{\beta}}}@{\mathbf{y}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\mathbf{c}_{3}+\boldsymbol{{\alpha}}}{\mathbf{d}_{3}+\boldsymbol{{\beta}}}@{\mathbf{u}}{\boldsymbol{{\Omega}}}\Riemannthetachar{\mathbf{c}_{4}+\boldsymbol{{\alpha}}}{\mathbf{d}_{4}+\boldsymbol{{\beta}}}@{\mathbf{v}}{\boldsymbol{{\Omega}}}.}

0 references

DLMF id

DLMF:21.6.E7

0 references

Symbols used

Riemann theta function with characteristics

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannthetachar{\NVar{\boldsymbol{{\alpha}}}}{\NVar{\boldsymbol{{\beta}}}}@{% \NVar{\mathbf{z}}}{\NVar{\boldsymbol{{\Omega}}}}}

xml-id

C21.S2.E5.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

test

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}

xml-id

C3.S12.E1.m2acdec

0 references