DLMF:19.7.E9 (Q6204): Difference between revisions

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Revision as of 13:41, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:41, 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
			Q11808
		Property / Symbols used: Q11808 / rank
			Normal rank
		Property / Symbols used: Q11808 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11808 / qualifier
			xml-id: C19.S1.XMD5.m1hdec
		Property / Symbols used
			Q11809
		Property / Symbols used: Q11809 / rank
			Normal rank
		Property / Symbols used: Q11809 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\alpha^{2}}}$ \alpha^{2}
		Property / Symbols used: Q11809 / qualifier
			xml-id: C19.S1.XMD7.m1edec
		Property / Symbols used
			Q11823
		Property / Symbols used: Q11823 / rank
			Normal rank
		Property / Symbols used: Q11823 / qualifier
			Defining formula: ${\displaystyle{\displaystyle c}}$ c
		Property / Symbols used: Q11823 / qualifier
			xml-id: C19.S7.XMD9.m1adec

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Latest revision as of 13:41, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.7.E9	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)+\Pi\left(\phi,\omega^{2},k\right)(k^{2}-\alpha^{2})\Pi\left(\phi,\alpha^{2},k\right)+(k^{2}-\omega^{2})\Pi\left(\phi,\omega^{2},k\right)=k^{2}F\left(\phi,k\right)-\alpha^{2}\omega^{2}\sqrt{c-1}R_{C}\left(c(c-k^{2}),(c-\alpha^{2})(c-\omega^{2})\right),}}$

0 references

DLMF id

DLMF:19.7.E9

0 references

Symbols defined

change of variable (locally)

0 references

constraint

${\displaystyle{\displaystyle(1-\alpha^{2})(1-\omega^{2})=1-k^{2}}}$

0 references

Symbols used

Carlson’s combination of inverse circular and inverse hyperbolic functions

Defining formula

${\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}$

xml-id

C19.S2.E17.m2aadec

0 references

Legendre’s incomplete elliptic integral of the first kind

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}$

xml-id

C19.S2.E4.m2addec

0 references

Legendre’s incomplete elliptic integral of the third kind

Defining formula

${\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}\right)}}$

xml-id

C19.S2.E7.m2addec

0 references

Q11807

Defining formula

${\displaystyle{\displaystyle\phi}}$

xml-id

C19.S1.XMD4.m1edec

0 references

Q11808

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C19.S1.XMD5.m1hdec

0 references

Q11809

Defining formula

${\displaystyle{\displaystyle\alpha^{2}}}$

xml-id

C19.S1.XMD7.m1edec

0 references

Q11823

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C19.S7.XMD9.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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