DLMF:19.4.E7 (Q6127): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 13:37, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:38, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(8 intermediate revisions by the same user not shown)
		Property / Symbols used
			Legendre’s incomplete elliptic integral of the second kind
		Property / Symbols used: Legendre’s incomplete elliptic integral of the second kind / rank
			Normal rank
		Property / Symbols used: Legendre’s incomplete elliptic integral of the second kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$ \incellintEk@{\NVar{\phi}}{\NVar{k}}
		Property / Symbols used: Legendre’s incomplete elliptic integral of the second kind / qualifier
			xml-id: C19.S2.E5.m2abdec
		Property / Symbols used
			Legendre’s incomplete elliptic integral of the third kind
		Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / rank
			Normal rank
		Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Pi\left(\NVar{\phi},\NVar{\alpha}^{2},\NVar{k}\right)}}$ \incellintPik@{\NVar{\phi}}{\NVar{\alpha}^{2}}{\NVar{k}}
		Property / Symbols used: Legendre’s incomplete elliptic integral of the third kind / qualifier
			xml-id: C19.S2.E7.m2adec
		Property / Symbols used
			partial derivative of $$f$$ with respect to $$x$$
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
			Normal rank
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$ \pderiv{\NVar{f}}{\NVar{x}}
		Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
			xml-id: C1.S5.E3.m4acdec
		Property / Symbols used
			partial differential of $$x$$
		Property / Symbols used: partial differential of $$x$$ / rank
			Normal rank
		Property / Symbols used: partial differential of $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\partial\NVar{x}}}$ \pdiff{\NVar{x}}
		Property / Symbols used: partial differential of $$x$$ / qualifier
			xml-id: C1.S5.E3.m2acdec
		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
			Q11807
		Property / Symbols used: Q11807 / rank
			Normal rank
		Property / Symbols used: Q11807 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\phi}}$ \phi
		Property / Symbols used: Q11807 / qualifier
			xml-id: C19.S1.XMD4.m1bdec
		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.m1fdec
		Property / Symbols used
			Q11815
		Property / Symbols used: Q11815 / rank
			Normal rank
		Property / Symbols used: Q11815 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k^{\prime}}}$ k^{\prime}
		Property / Symbols used: Q11815 / qualifier
			xml-id: C19.S1.XMD6.m1edec
		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.m1adec

---

Latest revision as of 13:38, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.4.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{\partial\Pi\left(\phi,\alpha^{2},k\right)}{\partial k}=\frac{k}{{k^{\prime}}^{2}(k^{2}-\alpha^{2})}\left({E\left(\phi,k\right)-{k^{\prime}}^{2}\Pi\left(\phi,\alpha^{2},k\right)}-\frac{k^{2}\sin\phi\cos\phi}{\sqrt{1-k^{2}{\sin^{2}}\phi}}\right).}}$

0 references

DLMF id

DLMF:19.4.E7

0 references

Symbols used

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

Legendre’s incomplete elliptic integral of the second kind

Defining formula

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

xml-id

C19.S2.E5.m2abdec

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.m2adec

0 references

partial derivative of $$f$$ with respect to $$x$$

Defining formula

${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$

xml-id

C1.S5.E3.m4acdec

0 references

partial differential of $$x$$

Defining formula

${\displaystyle{\displaystyle\partial\NVar{x}}}$

xml-id

C1.S5.E3.m2acdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2aadec

0 references

Q11807

Defining formula

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

xml-id

C19.S1.XMD4.m1bdec

0 references

Q11808

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C19.S1.XMD5.m1fdec

0 references

Q11815

Defining formula

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

xml-id

C19.S1.XMD6.m1edec

0 references

Q11809

Defining formula

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

xml-id

C19.S1.XMD7.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6127&oldid=38454"