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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
Defining formula:

ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2aadec

Revision as of 19:15, 1 January 2020

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DLMF:4.37.E14
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    Statements

    Defining formula
    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,}}
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    DLMF id
    DLMF:4.37.E14
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    constraint
    ℑ ⁡ z ≷ 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Im z\gtrless 0}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    inverse hyperbolic secant function
    Defining formula
    arcsech ⁡ z hyperbolic-inverse-secant 𝑧 {\displaystyle{\displaystyle\operatorname{arcsech}\NVar{z}}}
    xml-id
    C4.S37.E8.m2abdec
    0 references
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2aadec
    0 references
     
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