DLMF:19.14.E3 (Q6308): Difference between revisions

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Revision as of 13:50, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:51, 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
			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.m1abdec
		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.m2abdec
		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.m3abdec
		Property / Symbols used
			Q10897
		Property / Symbols used: Q10897 / rank
			Normal rank
		Property / Symbols used: Q10897 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}$ \sign@@{\NVar{x}}
		Property / Symbols used: Q10897 / qualifier
			xml-id: introduction.Sx4.p2.t1.r18.m6adec
		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 13:51, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.14.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{x}\frac{\mathrm{d}t}{\sqrt{1+t^{4}}}=\frac{\operatorname{sign}\left(x\right)}{2}F\left(\phi,k\right),}}$

0 references

DLMF id

DLMF:19.14.E3

0 references

constraint

${\displaystyle{\displaystyle\cos\phi=\dfrac{1-x^{2}}{1+x^{2}}}}$

0 references

${\displaystyle{\displaystyle\cos\phi=\dfrac{1-x^{2}}{1+x^{2}}}}$

0 references

${\displaystyle{\displaystyle k^{2}=\dfrac{1}{2}}}$

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Symbols used

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2abdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abdec

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.m2abdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abdec

0 references

Q10897

Defining formula

${\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}$

xml-id

introduction.Sx4.p2.t1.r18.m6adec

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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