DLMF:19.2.E6 (Q6087): Difference between revisions

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Revision as of 17:38, 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 13:35, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols defined
			incomplete elliptic integral of Legendre’s type
		Property / Symbols defined: incomplete elliptic integral of Legendre’s type / rank
			Normal rank
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1addec
		Property / Symbols used
			Legendre’s incomplete elliptic integral of the first kind
		Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / rank
			Normal rank
		Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / qualifier
			Defining formula: ${\displaystyle{\displaystyle F\left(\NVar{\phi},\NVar{k}\right)}}$ \incellintFk@{\NVar{\phi}}{\NVar{k}}
		Property / Symbols used: Legendre’s incomplete elliptic integral of the first kind / qualifier
			xml-id: C19.S2.E4.m2aadec
		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.m2aadec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3addec
		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.m2abdec
		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.m1bdec

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Latest revision as of 13:35, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.2.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle D\left(\phi,k\right)=\int_{0}^{\phi}\frac{{\sin^{2}}\theta\mathrm{d}\theta}{\sqrt{1-k^{2}{\sin^{2}}\theta}}=\int_{0}^{\sin\phi}\frac{t^{2}\mathrm{d}t}{\sqrt{1-t^{2}}\sqrt{1-k^{2}t^{2}}}=(F\left(\phi,k\right)-E\left(\phi,k\right))/k^{2}.}}$

0 references

DLMF id

DLMF:19.2.E6

0 references

Symbols defined

incomplete elliptic integral of Legendre’s type

0 references

Symbols used

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1addec

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.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.m2aadec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3addec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2abdec

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.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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