DLMF:14.15.E27 (Q4875): Difference between revisions

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Revision as of 01:53, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:53, 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
			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.m1cdec
		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.m1bdec
		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.m1jdec

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Latest revision as of 01:53, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E27	No description defined

Statements

Defining formula

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

0 references

DLMF id

DLMF:14.15.E27

0 references

constraint

${\displaystyle{\displaystyle\alpha\leq\zeta<\infty}}$

0 references

Symbols used

Q11246

Defining formula

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

xml-id

C4.S37.SS2.p1.m9adec

0 references

Q11248

Defining formula

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

xml-id

C4.S37.SS2.p1.m10adec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1qdec

0 references

Q11620

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C14.S15.XMD13.m1cdec

0 references

Q11621

Defining formula

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

xml-id

C14.S15.XMD14.m1bdec

0 references

Q11619

Defining formula

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

xml-id

C14.S15.XMD9.m1jdec

0 references

 

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