DLMF:4.37.E24 (Q1943): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11243 / rank
 
Normal rank
Property / Symbols used: Q11243 / qualifier
 
test:

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

[\NVar{a},\NVar{b})
Property / Symbols used: Q11243 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r1.m4aadec
Property / Symbols used
 
Property / Symbols used: Q10923 / rank
 
Normal rank
Property / Symbols used: Q10923 / qualifier
 
test:

ℂ {\displaystyle{\displaystyle\mathbb{C}}}

\Complexes
Property / Symbols used: Q10923 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2agdec
Property / Symbols used
 
Property / Symbols used: Q11248 / rank
 
Normal rank
Property / Symbols used: Q11248 / qualifier
 
test:

arctanh ⁡ z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}

\atanh@@{\NVar{z}}
Property / Symbols used: Q11248 / qualifier
 
xml-id: C4.S37.SS2.p1.m10acdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

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.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11244 / rank
 
Normal rank
Property / Symbols used: Q11244 / qualifier
 
test:

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

(\NVar{a},\NVar{b}]
Property / Symbols used: Q11244 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r1.m3acdec
Property / Symbols used
 
Property / Symbols used: Q10785 / rank
 
Normal rank
Property / Symbols used: Q10785 / qualifier
 
test:

∖ {\displaystyle{\displaystyle\setminus}}

\setminus
Property / Symbols used: Q10785 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r19.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10824 / rank
 
Normal rank
Property / Symbols used: Q10824 / qualifier
 
test:

∪ {\displaystyle{\displaystyle\cup}}

\cup
Property / Symbols used: Q10824 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r28.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1sdec

Latest revision as of 18:17, 1 January 2020

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Language Label Description Also known as
English
DLMF:4.37.E24
No description defined

    Statements

    test
    arctanh ⁡ z = 1 2 ⁢ ln ⁡ ( 1 + z 1 - z ) , hyperbolic-inverse-tangent 𝑧 1 2 1 𝑧 1 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}z=\tfrac{1}{2}\ln\left(\frac% {1+z}{1-z}\right),}}
    0 references
    DLMF id
    DLMF:4.37.E24
    0 references
    constraint
    z ∈ ℂ ∖ ( - ∞ , - 1 ] ∪ [ 1 , ∞ ) 𝑧 1 1 {\displaystyle{\displaystyle z\in\mathbb{C}\setminus(-\infty,-1]\cup[1,\infty)}}
    0 references
    Symbols used
    Q11243
    test
    [ a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p2.t1.r1.m4aadec
    0 references
    Q10923
    test
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2acdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2agdec
    0 references
    Q11248
    test
    arctanh ⁡ z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m10acdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ahdec
    0 references
    Q11244
    test
    ( a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p2.t1.r1.m3acdec
    0 references
    Q10785
    test
    ∖ {\displaystyle{\displaystyle\setminus}}
    xml-id
    introduction.Sx4.p2.t1.r19.m2acdec
    0 references
    Q10824
    test
    ∪ {\displaystyle{\displaystyle\cup}}
    xml-id
    introduction.Sx4.p1.t1.r28.m2aadec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1sdec
    0 references
     
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