DLMF:4.37.E21 (Q1940): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

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

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10777 / rank
 
Normal rank
Property / Symbols used: Q10777 / qualifier
 
Defining formula:

( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}

(\NVar{a},\NVar{b})
Property / Symbols used: Q10777 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r29.m6abdec
Property / Symbols used
 
Property / Symbols used: Q10785 / rank
 
Normal rank
Property / Symbols used: Q10785 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\setminus}}

\setminus
Property / Symbols used: Q10785 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r19.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1rdec

Latest revision as of 19:17, 1 January 2020

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DLMF:4.37.E21
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    Statements

    arccosh z = 2 ln ( ( z + 1 2 ) 1 / 2 + ( z - 1 2 ) 1 / 2 ) , hyperbolic-inverse-cosine 𝑧 2 superscript 𝑧 1 2 1 2 superscript 𝑧 1 2 1 2 {\displaystyle{\displaystyle\operatorname{arccosh}z=2\ln\left(\left(\frac{z+1}% {2}\right)^{1/2}+\left(\frac{z-1}{2}\right)^{1/2}\right),}}
    0 references
    DLMF:4.37.E21
    0 references
    z ( - , 1 ) 𝑧 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,1)}}
    0 references
    {\displaystyle{\displaystyle\mathbb{C}}}
    introduction.Sx4.p1.t1.r1.m2abdec
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    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2addec
    0 references
    arccosh z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    C4.S37.SS2.p1.m9aedec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aedec
    0 references
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    introduction.Sx4.p1.t1.r29.m6abdec
    0 references
    {\displaystyle{\displaystyle\setminus}}
    introduction.Sx4.p2.t1.r19.m2abdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1rdec
    0 references