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DLMF:4.24.E11 - MaRDI portal

DLMF:4.24.E11 (Q2091)

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DLMF:4.24.E11
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    Statements

    DLMF defining formula
    d d z ⁡ arcsec ⁡ z = ± 1 z ⁢ ( z 2 - 1 ) 1 / 2 , derivative 𝑧 𝑧 plus-or-minus 1 𝑧 superscript superscript 𝑧 2 1 1 2 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{arcsec% }z=\pm\frac{1}{z(z^{2}-1)^{1/2}},}}
    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 $$x$$
    DLMF 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.m2addec
    0 references
    arcsecant function
    DLMF defining formula
    arcsec ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsec}\NVar{z}}}
    xml-id
    C4.S23.E8.m2adec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1idec
    0 references

    Identifiers

     
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