DLMF:21.6.E4 (Q6892): Difference between revisions

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Revision as of 14:50, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:51, 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
			Q11966
		Property / Symbols used: Q11966 / rank
			Normal rank
		Property / Symbols used: Q11966 / qualifier
			Defining formula: ${\displaystyle{\displaystyle h}}$ h
		Property / Symbols used: Q11966 / qualifier
			xml-id: C21.S1.XMD2.m1cdec
		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.m1adec
		Property / Symbols used
			Q11968
		Property / Symbols used: Q11968 / rank
			Normal rank
		Property / Symbols used: Q11968 / qualifier
			Defining formula: ${\displaystyle{\displaystyle T_{jk}}}$ T_{jk}
		Property / Symbols used: Q11968 / qualifier
			xml-id: C21.S6.XMD1.m1adec
		Property / Symbols used
			set of matrices (locally)
		Property / Symbols used: set of matrices (locally) / rank
			Normal rank
		Property / Symbols used: set of matrices (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathcal{K}}}$ \mathcal{K}
		Property / Symbols used: set of matrices (locally) / qualifier
			xml-id: C21.S6.XMD2.m1bdec
		Property / Symbols used
			number of elements (locally)
		Property / Symbols used: number of elements (locally) / rank
			Normal rank
		Property / Symbols used: number of elements (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathcal{D}}}$ \mathcal{D}
		Property / Symbols used: number of elements (locally) / qualifier
			xml-id: C21.S6.XMD3.m1bdec

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Latest revision as of 14:51, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:21.6.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\prod_{j=1}^{h}\theta\genfrac{[}{]}{0.0pt}{}{\sum_{k=1}^{h}T_{jk}\mathbf{c}_{k}}{\sum_{k=1}^{h}T_{jk}\mathbf{d}_{k}}\left(\sum_{k=1}^{h}T_{jk}\mathbf{z}_{k}\middle|\boldsymbol{{\Omega}}\right)=\frac{1}{\mathcal{D}^{g}}\sum_{\mathbf{A}\in\mathcal{K}}\sum_{\mathbf{B}\in\mathcal{K}}e^{-2\pi i\sum_{j=1}^{h}\mathbf{b}_{j}\cdot\mathbf{c}_{j}}\prod_{j=1}^{h}\theta\genfrac{[}{]}{0.0pt}{}{\mathbf{a}_{j}+\mathbf{c}_{j}}{\mathbf{b}_{j}+\mathbf{d}_{j}}\left(\mathbf{z}_{j}\middle|\boldsymbol{{\Omega}}\right),}}$

0 references

DLMF id

DLMF:21.6.E4

0 references

Symbols used

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.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2aadec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aadec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

Q11959

Defining formula

${\displaystyle{\displaystyle g}}$

xml-id

C21.S1.XMD1.m1bdec

0 references

Q11966

Defining formula

${\displaystyle{\displaystyle h}}$

xml-id

C21.S1.XMD2.m1cdec

0 references

Q11960

Defining formula

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

xml-id

C21.S1.XMD3.m1adec

0 references

Q11968

Defining formula

${\displaystyle{\displaystyle T_{jk}}}$

xml-id

C21.S6.XMD1.m1adec

0 references

set of matrices (locally)

Defining formula

${\displaystyle{\displaystyle\mathcal{K}}}$

xml-id

C21.S6.XMD2.m1bdec

0 references

number of elements (locally)

Defining formula

${\displaystyle{\displaystyle\mathcal{D}}}$

xml-id

C21.S6.XMD3.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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