DLMF:4.23.E21 (Q1773): Difference between revisions

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Revision as of 18:32, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 18:32, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2afdec
		Property / Symbols used
			Q11242
		Property / Symbols used: Q11242 / rank
			Normal rank
		Property / Symbols used: Q11242 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}$ \asin@@{\NVar{z}}
		Property / Symbols used: Q11242 / qualifier
			xml-id: C4.S23.SS2.p1.m5afdec
		Property / Symbols used
			principal branch of logarithm function
		Property / Symbols used: principal branch of logarithm function / rank
			Normal rank
		Property / Symbols used: principal branch of logarithm function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\ln\NVar{z}}}$ \ln@@{\NVar{z}}
		Property / Symbols used: principal branch of logarithm function / qualifier
			xml-id: C4.S2.E2.m2abdec
		Property / Symbols used
			Q11244
		Property / Symbols used: Q11244 / rank
			Normal rank
		Property / Symbols used: Q11244 / qualifier
			Defining formula: ${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$ (\NVar{a},\NVar{b}]
		Property / Symbols used: Q11244 / qualifier
			xml-id: introduction.Sx4.p2.t1.r1.m3adec
		Property / Symbols used
			Q11218
		Property / Symbols used: Q11218 / rank
			Normal rank
		Property / Symbols used: Q11218 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11218 / qualifier
			xml-id: C4.S1.XMD6.m1adec

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Latest revision as of 18:32, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:4.23.E21	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{arcsin}x=-\tfrac{1}{2}\pi\pm i\ln\left((x^{2}-1)^{1/2}-x\right),}}$

0 references

DLMF id

DLMF:4.23.E21

0 references

constraint

${\displaystyle{\displaystyle x\in(-\infty,-1]}}$

0 references

Symbols used

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2afdec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2abdec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2afdec

0 references

Q11242

Defining formula

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

xml-id

C4.S23.SS2.p1.m5afdec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2abdec

0 references

Q11244

Defining formula

${\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}$

xml-id

introduction.Sx4.p2.t1.r1.m3adec

0 references

Q11218

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C4.S1.XMD6.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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