DLMF:22.6.E7 (Q6941): Difference between revisions

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Revision as of 14:57, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:57, 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: ${\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}$ \Jacobielldnk@{\NVar{z}}{\NVar{k}}
		Property / Symbols used: Jacobian elliptic function / qualifier
			xml-id: C22.S2.E6.m2acdec
		Property / Symbols used
			Jacobian elliptic function
		Property / Symbols used: Jacobian elliptic function / rank
			Normal rank
		Property / Symbols used: Jacobian elliptic function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$ \Jacobiellsnk@{\NVar{z}}{\NVar{k}}
		Property / Symbols used: Jacobian elliptic function / qualifier
			xml-id: C22.S2.E4.m2acdec
		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.m1fdec
		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.m1fdec
		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

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Latest revision as of 14:57, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:22.6.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{dn}\left(2z,k\right)=\frac{{\operatorname{dn}^{2}}\left(z,k\right)-k^{2}{\operatorname{sn}^{2}}\left(z,k\right){\operatorname{cn}^{2}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)}=\frac{{\operatorname{dn}^{4}}\left(z,k\right)+k^{2}{k^{\prime}}^{2}{\operatorname{sn}^{4}}\left(z,k\right)}{1-k^{2}{\operatorname{sn}^{4}}\left(z,k\right)}.}}$

0 references

DLMF id

DLMF:22.6.E7

0 references

Symbols used

Jacobian elliptic function

Defining formula

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

xml-id

C22.S2.E5.m2acdec

0 references

Jacobian elliptic function

Defining formula

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

xml-id

C22.S2.E6.m2acdec

0 references

Jacobian elliptic function

Defining formula

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

xml-id

C22.S2.E4.m2acdec

0 references

Q11985

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C22.S1.XMD3.m1fdec

0 references

Q11984

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C22.S1.XMD4.m1fdec

0 references

Q11988

Defining formula

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

xml-id

C22.S1.XMD5.m1cdec

0 references

 

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