DLMF:22.12.E3 (Q7041): Difference between revisions

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Revision as of 15:15, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:16, 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
			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.m2aadec
		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.m1abdec
		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.m2aadec
		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.m2aadec
		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.m1bdec
		Property / Symbols used
			Q11987
		Property / Symbols used: Q11987 / rank
			Normal rank
		Property / Symbols used: Q11987 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tau}}$ \tau
		Property / Symbols used: Q11987 / qualifier
			xml-id: C22.S1.XMD6.m1bdec

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Latest revision as of 15:16, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:22.12.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle 2iKk\operatorname{cn}\left(2Kt,k\right)=\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin\left(\pi(t-(n+\frac{1}{2})\tau)\right)}=\sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-(n+\frac{1}{2})\tau}\right),}}$

0 references

DLMF id

DLMF:22.12.E3

0 references

Symbols used

Jacobian elliptic function

Defining formula

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

xml-id

C22.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

Q11600

Defining formula

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

xml-id

C19.S2.E8.m1abdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2aadec

0 references

Q11984

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C22.S1.XMD4.m1bdec

0 references

Q11987

Defining formula

${\displaystyle{\displaystyle\tau}}$

xml-id

C22.S1.XMD6.m1bdec

0 references

 

Sitelinks

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