DLMF:21.2.E6 (Q6862): Difference between revisions

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Revision as of 14:47, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:47, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2aedec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2addec
		Property / Symbols used
			Q11960
		Property / Symbols used: Q11960 / rank
			Normal rank
		Property / Symbols used: Q11960 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{{\Omega}}}}$ \boldsymbol{{\Omega}}
		Property / Symbols used: Q11960 / qualifier
			xml-id: C21.S1.XMD3.m1cdec
		Property / Symbols used
			Q11961
		Property / Symbols used: Q11961 / rank
			Normal rank
		Property / Symbols used: Q11961 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}$ \boldsymbol{{\alpha}}
		Property / Symbols used: Q11961 / qualifier
			xml-id: C21.S1.XMD4.m1adec
		Property / Symbols used
			Q11962
		Property / Symbols used: Q11962 / rank
			Normal rank
		Property / Symbols used: Q11962 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{{\beta}}}}$ \boldsymbol{{\beta}}
		Property / Symbols used: Q11962 / qualifier
			xml-id: C21.S1.XMD5.m1adec

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Latest revision as of 14:47, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:21.2.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\boldsymbol{{\alpha}}}{\boldsymbol{{\beta}}}\left(\mathbf{z}\middle|\boldsymbol{{\Omega}}\right)=e^{2\pi i\left(\frac{1}{2}\boldsymbol{{\alpha}}\cdot\boldsymbol{{\Omega}}\cdot\boldsymbol{{\alpha}}+\boldsymbol{{\alpha}}\cdot[\mathbf{z}+\boldsymbol{{\beta}}]\right)}\theta\left(\mathbf{z}+\boldsymbol{{\Omega}}\boldsymbol{{\alpha}}+\boldsymbol{{\beta}}\middle|\boldsymbol{{\Omega}}\right),}}$

0 references

DLMF id

DLMF:21.2.E6

0 references

Symbols used

Riemann theta function

Defining formula

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

xml-id

C21.S2.E1.m2acdec

0 references

Riemann theta function with characteristics

Defining formula

${\displaystyle{\displaystyle\theta\genfrac{[}{]}{0.0pt}{}{\NVar{\boldsymbol{{\alpha}}}}{\NVar{\boldsymbol{{\beta}}}}\left(\middle|missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$

xml-id

C21.S2.E5.m2aadec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2aedec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aedec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2addec

0 references

Q11960

Defining formula

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

xml-id

C21.S1.XMD3.m1cdec

0 references

Q11961

Defining formula

${\displaystyle{\displaystyle\boldsymbol{{\alpha}}}}$

xml-id

C21.S1.XMD4.m1adec

0 references

Q11962

Defining formula

${\displaystyle{\displaystyle\boldsymbol{{\beta}}}}$

xml-id

C21.S1.XMD5.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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