DLMF:4.23.E42 (Q1794): Difference between revisions

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Revision as of 18:37, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 18:37, 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
			cotangent function
		Property / Symbols used: cotangent function / rank
			Normal rank
		Property / Symbols used: cotangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cot\NVar{z}}}$ \cot@@{\NVar{z}}
		Property / Symbols used: cotangent function / qualifier
			xml-id: C4.S14.E7.m2adec
		Property / Symbols used
			inverse hyperbolic cosecant function
		Property / Symbols used: inverse hyperbolic cosecant function / rank
			Normal rank
		Property / Symbols used: inverse hyperbolic cosecant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arccsch}\NVar{z}}}$ \acsch@@{\NVar{z}}
		Property / Symbols used: inverse hyperbolic cosecant function / qualifier
			xml-id: C4.S37.E7.m2adec
		Property / Symbols used
			Q11246
		Property / Symbols used: Q11246 / rank
			Normal rank
		Property / Symbols used: Q11246 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}$ \acosh@@{\NVar{z}}
		Property / Symbols used: Q11246 / qualifier
			xml-id: C4.S37.SS2.p1.m9adec
		Property / Symbols used
			inverse hyperbolic cotangent function
		Property / Symbols used: inverse hyperbolic cotangent function / rank
			Normal rank
		Property / Symbols used: inverse hyperbolic cotangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arccoth}\NVar{z}}}$ \acoth@@{\NVar{z}}
		Property / Symbols used: inverse hyperbolic cotangent function / qualifier
			xml-id: C4.S37.E9.m2adec
		Property / Symbols used
			inverse hyperbolic secant function
		Property / Symbols used: inverse hyperbolic secant function / rank
			Normal rank
		Property / Symbols used: inverse hyperbolic secant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}$ \asech@@{\NVar{z}}
		Property / Symbols used: inverse hyperbolic secant function / qualifier
			xml-id: C4.S37.E8.m2adec
		Property / Symbols used
			Q11247
		Property / Symbols used: Q11247 / rank
			Normal rank
		Property / Symbols used: Q11247 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}$ \asinh@@{\NVar{z}}
		Property / Symbols used: Q11247 / qualifier
			xml-id: C4.S37.SS2.p1.m8adec
		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.m10adec
		Property / Symbols used
			inverse Gudermannian function
		Property / Symbols used: inverse Gudermannian function / rank
			Normal rank
		Property / Symbols used: inverse Gudermannian function / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}$ \aGudermannian@{\NVar{x}}
		Property / Symbols used: inverse Gudermannian function / qualifier
			xml-id: C4.S23.E41.m2aadec
		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.m2aldec
		Property / Symbols used
			secant function
		Property / Symbols used: secant function / rank
			Normal rank
		Property / Symbols used: secant function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sec\NVar{z}}}$ \sec@@{\NVar{z}}
		Property / Symbols used: secant function / qualifier
			xml-id: C4.S14.E6.m2aadec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2aadec
		Property / Symbols used
			tangent function
		Property / Symbols used: tangent function / rank
			Normal rank
		Property / Symbols used: tangent function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\tan\NVar{z}}}$ \tan@@{\NVar{z}}
		Property / Symbols used: tangent function / qualifier
			xml-id: C4.S14.E4.m2aadec
		Property / Symbols used
			Q11218
		Property / Symbols used: Q11218 / rank
			Normal rank
		Property / Symbols used: Q11218 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11218 / qualifier
			xml-id: C4.S1.XMD6.m1mdec

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Latest revision as of 18:37, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:4.23.E42	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(x\right)=\ln\tan\left(\tfrac{1}{2}x+\tfrac{1}{4}\pi\right)=\ln\left(\sec x+\tan x\right)=\operatorname{arcsinh}\left(\tan x\right)=\operatorname{arccsch}\left(\cot x\right)=\operatorname{arccosh}\left(\sec x\right)=\operatorname{arcsech}\left(\cos x\right)=\operatorname{arctanh}\left(\sin x\right)=\operatorname{arccoth}\left(\csc x\right).}}$

0 references

DLMF id

DLMF:4.23.E42

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.m2apdec

0 references

cosecant function

Defining formula

${\displaystyle{\displaystyle\csc\NVar{z}}}$

xml-id

C4.S14.E5.m2adec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2aadec

0 references

cotangent function

Defining formula

${\displaystyle{\displaystyle\cot\NVar{z}}}$

xml-id

C4.S14.E7.m2adec

0 references

inverse hyperbolic cosecant function

Defining formula

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

xml-id

C4.S37.E7.m2adec

0 references

Q11246

Defining formula

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

xml-id

C4.S37.SS2.p1.m9adec

0 references

inverse hyperbolic cotangent function

Defining formula

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

xml-id

C4.S37.E9.m2adec

0 references

inverse hyperbolic secant function

Defining formula

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

xml-id

C4.S37.E8.m2adec

0 references

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.m10adec

0 references

inverse Gudermannian function

Defining formula

${\displaystyle{\displaystyle{\operatorname{gd}^{-1}}\left(\NVar{x}\right)}}$

xml-id

C4.S23.E41.m2aadec

0 references

principal branch of logarithm function

Defining formula

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

xml-id

C4.S2.E2.m2aldec

0 references

secant function

Defining formula

${\displaystyle{\displaystyle\sec\NVar{z}}}$

xml-id

C4.S14.E6.m2aadec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2aadec

0 references

tangent function

Defining formula

${\displaystyle{\displaystyle\tan\NVar{z}}}$

xml-id

C4.S14.E4.m2aadec

0 references

Q11218

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C4.S1.XMD6.m1mdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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