DLMF:4.37.E22 (Q1941): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1dec

Latest revision as of 19:17, 1 January 2020

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DLMF:4.37.E22
No description defined

    Statements

    Defining formula
    arccosh ⁡ x = ± ln ⁡ ( i ⁢ ( 1 - x 2 ) 1 / 2 + x ) , hyperbolic-inverse-cosine 𝑥 plus-or-minus 𝑖 superscript 1 superscript 𝑥 2 1 2 𝑥 {\displaystyle{\displaystyle\operatorname{arccosh}x=\pm\ln\left(i(1-x^{2})^{1/% 2}+x\right),}}
    0 references
    DLMF id
    DLMF:4.37.E22
    0 references
    constraint
    x ∈ ( - 1 , 1 ] 𝑥 1 1 {\displaystyle{\displaystyle x\in(-1,1]}}
    0 references
    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aedec
    0 references
    Q11246
    Defining formula
    arccosh ⁡ z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m9afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2afdec
    0 references
    Q11244
    Defining formula
    ( a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p2.t1.r1.m3aadec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1dec
    0 references
     
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