DLMF:4.37.E20 (Q1939): Difference between revisions

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Revision as of 19:16, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 19:16, 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.m2aedec
		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.m2addec
		Property / Symbols used
			Q11222
		Property / Symbols used: Q11222 / rank
			Normal rank
		Property / Symbols used: Q11222 / qualifier
			Defining formula: ${\displaystyle{\displaystyle y}}$ y
		Property / Symbols used: Q11222 / qualifier
			xml-id: C4.S1.XMD7.m1bdec

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Latest revision as of 19:16, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:4.37.E20	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\operatorname{arccosh}\left(\mathrm{i}y\right)=\pm\tfrac{1}{2}\pi\mathrm{i}+\ln\left((y^{2}+1)^{1/2}\pm y\right),}}$

0 references

DLMF id

DLMF:4.37.E20

0 references

constraint

${\displaystyle{\displaystyle y\gtrless 0}}$

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.m2addec

0 references

Q11246

Defining formula

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

xml-id

C4.S37.SS2.p1.m9addec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aedec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2addec

0 references

Q11222

Defining formula

${\displaystyle{\displaystyle y}}$

xml-id

C4.S1.XMD7.m1bdec

0 references

 

Sitelinks

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