DLMF:14.15.E28 (Q4876): Difference between revisions

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Revision as of 13:20, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:20, 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
			Q11589
		Property / Symbols used: Q11589 / rank
			Normal rank
		Property / Symbols used: Q11589 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11589 / qualifier
			xml-id: C14.S1.XMD1.m1rdec
		Property / Symbols used
			Q11620
		Property / Symbols used: Q11620 / rank
			Normal rank
		Property / Symbols used: Q11620 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11620 / qualifier
			xml-id: C14.S15.XMD13.m1ddec
		Property / Symbols used
			Q11621
		Property / Symbols used: Q11621 / rank
			Normal rank
		Property / Symbols used: Q11621 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\zeta}}$ \zeta
		Property / Symbols used: Q11621 / qualifier
			xml-id: C14.S15.XMD14.m1cdec
		Property / Symbols used
			Q11619
		Property / Symbols used: Q11619 / rank
			Normal rank
		Property / Symbols used: Q11619 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\alpha}}$ \alpha
		Property / Symbols used: Q11619 / qualifier
			xml-id: C14.S15.XMD9.m1kdec

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Latest revision as of 13:20, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E28	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{1}{2}\alpha^{2}\operatorname{arcsin}\left(\frac{\zeta}{\alpha}\right)+\frac{1}{2}\zeta\left(\alpha^{2}-\zeta^{2}\right)^{1/2}=\operatorname{arcsin}\left(\frac{x}{a}\right)-\left(1-a^{2}\right)^{1/2}\operatorname{arctan}\left(x\left(\frac{1-a^{2}}{a^{2}-x^{2}}\right)^{1/2}\right),}}$

0 references

DLMF id

DLMF:14.15.E28

0 references

constraint

${\displaystyle{\displaystyle-\alpha\leq\zeta\leq\alpha}}$

0 references

Symbols used

Q11242

Defining formula

${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$

xml-id

C4.S23.SS2.p1.m5adec

0 references

Q10816

Defining formula

${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$

xml-id

C4.S23.SS2.p1.m7aadec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1rdec

0 references

Q11620

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C14.S15.XMD13.m1ddec

0 references

Q11621

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C14.S15.XMD14.m1cdec

0 references

Q11619

Defining formula

${\displaystyle{\displaystyle\alpha}}$

xml-id

C14.S15.XMD9.m1kdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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