DLMF:21.6.E3 (Q6891): 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 14:50, 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
			Q11967
		Property / Symbols used: Q11967 / rank
			Normal rank
		Property / Symbols used: Q11967 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{tr}\NVar{\mathbf{A}}}}$ \trace\NVar{\mathbf{A}}
		Property / Symbols used: Q11967 / qualifier
			xml-id: introduction.Sx4.p2.t1.r7.m3adec
		Property / Symbols used
			Q11959
		Property / Symbols used: Q11959 / rank
			Normal rank
		Property / Symbols used: Q11959 / qualifier
			Defining formula: ${\displaystyle{\displaystyle g}}$ g
		Property / Symbols used: Q11959 / qualifier
			xml-id: C21.S1.XMD1.m1adec
		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.m1bdec
		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.m1dec
		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.m1dec
		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.m1adec
		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.m1adec

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Latest revision as of 14:50, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:21.6.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\prod_{j=1}^{h}\theta\left(\sum_{k=1}^{h}T_{jk}\mathbf{z}_{k}\middle|\boldsymbol{{\Omega}}\right)=\frac{1}{\mathcal{D}^{g}}\sum_{\mathbf{A}\in\mathcal{K}}\sum_{\mathbf{B}\in\mathcal{K}}e^{2\pi i\operatorname{tr}\left[\frac{1}{2}\mathbf{A}^{\mathrm{T}}\boldsymbol{{\Omega}}\mathbf{A}+\mathbf{A}^{\mathrm{T}}[\mathbf{Z}+\mathbf{B}]\right]}\*\prod_{j=1}^{h}\theta\left(\mathbf{z}_{j}+\boldsymbol{{\Omega}}\mathbf{a}_{j}+\mathbf{b}_{j}\middle|\boldsymbol{{\Omega}}\right),}}$

0 references

DLMF id

DLMF:21.6.E3

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.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2adec

0 references

Q10784

Defining formula

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

xml-id

introduction.Sx4.p1.t1.r10.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

0 references

Q11967

Defining formula

${\displaystyle{\displaystyle\operatorname{tr}\NVar{\mathbf{A}}}}$

xml-id

introduction.Sx4.p2.t1.r7.m3adec

0 references

Q11959

Defining formula

${\displaystyle{\displaystyle g}}$

xml-id

C21.S1.XMD1.m1adec

0 references

Q11966

Defining formula

${\displaystyle{\displaystyle h}}$

xml-id

C21.S1.XMD2.m1bdec

0 references

Q11960

Defining formula

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

xml-id

C21.S1.XMD3.m1dec

0 references

Q11968

Defining formula

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

xml-id

C21.S6.XMD1.m1dec

0 references

set of matrices (locally)

Defining formula

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

xml-id

C21.S6.XMD2.m1adec

0 references

number of elements (locally)

Defining formula

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

xml-id

C21.S6.XMD3.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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