DLMF:4.38.E12 (Q1962): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1jdec

Latest revision as of 19:20, 1 January 2020

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DLMF:4.38.E12
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    Statements

    Defining formula
    d d z ⁡ arccsch ⁡ z = ∓ 1 z ⁢ ( 1 + z 2 ) 1 / 2 , derivative 𝑧 hyperbolic-inverse-cosecant 𝑧 minus-or-plus 1 𝑧 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% arccsch}z=\mp\frac{1}{z(1+z^{2})^{1/2}},}}
    0 references
    DLMF id
    DLMF:4.38.E12
    0 references
    constraint
    ℜ ⁡ z ≷ 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}}
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    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2acdec
    0 references
    inverse hyperbolic cosecant function
    Defining formula
    arccsch ⁡ z hyperbolic-inverse-cosecant 𝑧 {\displaystyle{\displaystyle\operatorname{arccsch}\NVar{z}}}
    xml-id
    C4.S37.E7.m2adec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1addec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1jdec
    0 references
     
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