DLMF:4.37.E14 (Q1933): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.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.m1ndec

Latest revision as of 18:15, 1 January 2020

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DLMF:4.37.E14
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    Statements

    test
    arcsech ⁡ ( - z ) = ∓ π ⁢ i + arcsech ⁡ z , hyperbolic-inverse-secant 𝑧 minus-or-plus 𝜋 𝑖 hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\left(-z\right)=\mp\pi i+% \operatorname{arcsech}z,}}
    0 references
    DLMF id
    DLMF:4.37.E14
    0 references
    constraint
    ℑ ⁡ z ≷ 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Im z\gtrless 0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    inverse hyperbolic secant function
    test
    arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    xml-id
    C4.S37.E8.m2abdec
    0 references
    Q10901
    test
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2aadec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1ndec
    0 references
     
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