DLMF:22.11.E12 (Q7036): Difference between revisions

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Revision as of 22:41, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 15:14, 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
			Jacobian elliptic function
		Property / Symbols used: Jacobian elliptic function / rank
			Normal rank
		Property / Symbols used: Jacobian elliptic function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}$ \Jacobiellsck@{\NVar{z}}{\NVar{k}}
		Property / Symbols used: Jacobian elliptic function / qualifier
			xml-id: C22.S2.E9.m2adec
		Property / Symbols used
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2akdec
		Property / Symbols used
			Q11600
		Property / Symbols used: Q11600 / rank
			Normal rank
		Property / Symbols used: Q11600 / qualifier
			Defining formula: ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$ \compellintKk@{\NVar{k}}
		Property / Symbols used: Q11600 / qualifier
			xml-id: C19.S2.E8.m1akdec
		Property / Symbols used
			nome
		Property / Symbols used: nome / rank
			Normal rank
		Property / Symbols used: nome / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: nome / qualifier
			xml-id: C22.S2.E1.m2akdec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aedec
		Property / Symbols used
			tangent function
		Property / Symbols used: tangent function / rank
			Normal rank
		Property / Symbols used: tangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tan\NVar{z}}}$ \tan@@{\NVar{z}}
		Property / Symbols used: tangent function / qualifier
			xml-id: C4.S14.E4.m2adec
		Property / Symbols used
			Q11985
		Property / Symbols used: Q11985 / rank
			Normal rank
		Property / Symbols used: Q11985 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11985 / qualifier
			xml-id: C22.S1.XMD3.m1kdec
		Property / Symbols used
			Q11984
		Property / Symbols used: Q11984 / rank
			Normal rank
		Property / Symbols used: Q11984 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11984 / qualifier
			xml-id: C22.S1.XMD4.m1kdec
		Property / Symbols used
			Q11988
		Property / Symbols used: Q11988 / rank
			Normal rank
		Property / Symbols used: Q11988 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k^{\prime}}}$ k^{\prime}
		Property / Symbols used: Q11988 / qualifier
			xml-id: C22.S1.XMD5.m1cdec
		Property / Symbols used
			Q11986
		Property / Symbols used: Q11986 / rank
			Normal rank
		Property / Symbols used: Q11986 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: Q11986 / qualifier
			xml-id: C22.S2.XMD2.m1kdec

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Latest revision as of 15:14, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:22.11.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{sc}\left(z,k\right)-\frac{\pi}{2Kk^{\prime}}\tan\zeta=\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin\left(2n\zeta\right)}{1+q^{2n}}.}}$

0 references

DLMF id

DLMF:22.11.E12

0 references

Symbols used

Jacobian elliptic function

Defining formula

${\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}$

xml-id

C22.S2.E9.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2akdec

0 references

Q11600

Defining formula

${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$

xml-id

C19.S2.E8.m1akdec

0 references

nome

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C22.S2.E1.m2akdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aedec

0 references

tangent function

Defining formula

${\displaystyle{\displaystyle\tan\NVar{z}}}$

xml-id

C4.S14.E4.m2adec

0 references

Q11985

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C22.S1.XMD3.m1kdec

0 references

Q11984

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C22.S1.XMD4.m1kdec

0 references

Q11988

Defining formula

${\displaystyle{\displaystyle k^{\prime}}}$

xml-id

C22.S1.XMD5.m1cdec

0 references

Q11986

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C22.S2.XMD2.m1kdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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