DLMF:14.15.E31 (Q4879): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 13:21, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:21, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(3 intermediate revisions by the same user not shown)
		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.m1udec
		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.m1fdec
		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.m1fdec
		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.m1mdec

---

Latest revision as of 13:21, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.15.E31	No description defined

Statements

Defining formula

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

0 references

DLMF id

DLMF:14.15.E31

0 references

constraint

${\displaystyle{\displaystyle-\infty<\zeta<\infty}}$

0 references

Symbols used

Q11247

Defining formula

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

xml-id

C4.S37.SS2.p1.m8adec

0 references

Q11248

Defining formula

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

xml-id

C4.S37.SS2.p1.m10aadec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1udec

0 references

Q11620

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C14.S15.XMD13.m1fdec

0 references

Q11621

Defining formula

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

xml-id

C14.S15.XMD14.m1fdec

0 references

Q11619

Defining formula

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

xml-id

C14.S15.XMD9.m1mdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4879&oldid=35742"