DLMF:4.37.E19 (Q1938): 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.m2acdec
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.m6aadec
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.m2aadec
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.m1qdec

Latest revision as of 19:16, 1 January 2020

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DLMF:4.37.E19
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    Statements

    arccosh z = ln ( ± ( z 2 - 1 ) 1 / 2 + z ) , hyperbolic-inverse-cosine 𝑧 plus-or-minus superscript superscript 𝑧 2 1 1 2 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}z=\ln\left(\pm(z^{2}-1)^{1/2% }+z\right),}}
    0 references
    DLMF:4.37.E19
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    z ( - , 1 ) 𝑧 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,1)}}
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    {\displaystyle{\displaystyle\mathbb{C}}}
    introduction.Sx4.p1.t1.r1.m2aadec
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    {\displaystyle{\displaystyle\in}}
    introduction.Sx4.p1.t1.r10.m2acdec
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    arccosh z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    C4.S37.SS2.p1.m9acdec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2acdec
    0 references
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    introduction.Sx4.p1.t1.r29.m6aadec
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    {\displaystyle{\displaystyle\setminus}}
    introduction.Sx4.p2.t1.r19.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1qdec
    0 references