DLMF:14.20.E24 (Q4945): Difference between revisions

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Revision as of 15:43, 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 13:37, 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
			Q10816
		Property / Symbols used: Q10816 / rank
			Normal rank
		Property / Symbols used: Q10816 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}$ \atan@@{\NVar{z}}
		Property / Symbols used: Q10816 / qualifier
			xml-id: C4.S23.SS2.p1.m7abdec
		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
		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.m1xdec
		Property / Symbols used
			Q11636
		Property / Symbols used: Q11636 / rank
			Normal rank
		Property / Symbols used: Q11636 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\beta}}$ \beta
		Property / Symbols used: Q11636 / qualifier
			xml-id: C14.S20.XMD8.m1bdec
		Property / Symbols used
			Q11637
		Property / Symbols used: Q11637 / rank
			Normal rank
		Property / Symbols used: Q11637 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\rho}}$ \rho
		Property / Symbols used: Q11637 / qualifier
			xml-id: C14.S20.XMD9.m1adec

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Latest revision as of 13:37, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.20.E24	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\rho=\frac{1}{2}\ln\left(\frac{\left(1-\beta^{2}\right)x^{2}+1+\beta^{2}+2x\left(1+\beta^{2}-\beta^{2}x^{2}\right)^{1/2}}{1-x^{2}}\right)+\beta\operatorname{arctan}\left(\frac{\beta x}{\sqrt{1+\beta^{2}-\beta^{2}x^{2}}}\right)-\frac{1}{2}\ln\left(1+\beta^{2}\right),}}$

0 references

DLMF id

DLMF:14.20.E24

0 references

Symbols used

Q10816

Defining formula

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

xml-id

C4.S23.SS2.p1.m7abdec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2aadec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1xdec

0 references

Q11636

Defining formula

${\displaystyle{\displaystyle\beta}}$

xml-id

C14.S20.XMD8.m1bdec

0 references

Q11637

Defining formula

${\displaystyle{\displaystyle\rho}}$

xml-id

C14.S20.XMD9.m1adec

0 references

 

Sitelinks

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DRMF related sites(0 entries)

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