DLMF:19.2.E20 (Q6116): Difference between revisions

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Revision as of 17:39, 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 13:36, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle y<0\leq x}}$ y<0\leq x
		Property / constraint: ${\displaystyle{\displaystyle y<0\leq x}}$ / rank
			Normal rank
		Property / Symbols used
			Carlson’s combination of inverse circular and inverse hyperbolic functions
		Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / rank
			Normal rank
		Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
			Defining formula: ${\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}$ \CarlsonellintRC@{\NVar{x}}{\NVar{y}}
		Property / Symbols used: Carlson’s combination of inverse circular and inverse hyperbolic functions / qualifier
			xml-id: C19.S2.E17.m2acdec
		Property / Symbols used
			Q11248
		Property / Symbols used: Q11248 / rank
			Normal rank
		Property / Symbols used: Q11248 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}$ \atanh@@{\NVar{z}}
		Property / Symbols used: Q11248 / qualifier
			xml-id: C4.S37.SS2.p1.m10aadec
		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.m2aadec

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Latest revision as of 13:36, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:19.2.E20	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle R_{C}\left(x,y\right)=\sqrt{\frac{x}{x-y}}R_{C}\left(x-y,-y\right)=\frac{1}{\sqrt{x-y}}\operatorname{arctanh}\sqrt{\frac{x}{x-y}}=\frac{1}{\sqrt{x-y}}\ln\frac{\sqrt{x}+\sqrt{x-y}}{\sqrt{-y}},}}$

0 references

DLMF id

DLMF:19.2.E20

0 references

constraint

${\displaystyle{\displaystyle y<0\leq x}}$

0 references

Symbols used

Carlson’s combination of inverse circular and inverse hyperbolic functions

Defining formula

${\displaystyle{\displaystyle R_{C}\left(\NVar{x},\NVar{y}\right)}}$

xml-id

C19.S2.E17.m2acdec

0 references

Q11248

Defining formula

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

xml-id

C4.S37.SS2.p1.m10aadec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2aadec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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