DLMF:4.37.E16 (Q1935): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11247 / rank
 
Normal rank
Property / Symbols used: Q11247 / qualifier
 
Defining formula:

arcsinh ⁡ z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}

\asinh@@{\NVar{z}}
Property / Symbols used: Q11247 / qualifier
 
xml-id: C4.S37.SS2.p1.m8acdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec
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.m2adec
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.m6adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10824 / rank
 
Normal rank
Property / Symbols used: Q10824 / qualifier
 
Defining formula:

∪ {\displaystyle{\displaystyle\cup}}

\cup
Property / Symbols used: Q10824 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r28.m2adec
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.m1pdec

Latest revision as of 19:15, 1 January 2020

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DLMF:4.37.E16
No description defined

    Statements

    Defining formula
    arcsinh ⁡ z = ln ⁡ ( ( z 2 + 1 ) 1 / 2 + z ) , hyperbolic-inverse-sine 𝑧 superscript superscript 𝑧 2 1 1 2 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}z=\ln\left((z^{2}+1)^{1/2}+z% \right),}}
    0 references
    DLMF id
    DLMF:4.37.E16
    0 references
    constraint
    z / i ∈ ℂ ∖ ( - ∞ , - 1 ) ∪ ( 1 , ∞ ) 𝑧 𝑖 1 1 {\displaystyle{\displaystyle z/i\in\mathbb{C}\setminus(-\infty,-1)\cup(1,% \infty)}}
    0 references
    Symbols used
    Q10923
    Defining formula
    ℂ {\displaystyle{\displaystyle\mathbb{C}}}
    xml-id
    introduction.Sx4.p1.t1.r1.m2adec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    Q11247
    Defining formula
    arcsinh ⁡ z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m8acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6adec
    0 references
    Q10785
    Defining formula
    ∖ {\displaystyle{\displaystyle\setminus}}
    xml-id
    introduction.Sx4.p2.t1.r19.m2adec
    0 references
    Q10824
    Defining formula
    ∪ {\displaystyle{\displaystyle\cup}}
    xml-id
    introduction.Sx4.p1.t1.r28.m2adec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1pdec
    0 references
     
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