DLMF:4.37.E30 (Q1949)

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DLMF:4.37.E30
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    Statements

    Defining formula
    w = Arccosh ⁡ z = ± arccosh ⁡ z + 2 ⁢ k ⁢ π ⁢ i , 𝑤 multivalued-hyperbolic-inverse-cosine 𝑧 plus-or-minus hyperbolic-inverse-cosine 𝑧 2 𝑘 𝜋 𝑖 {\displaystyle{\displaystyle w=\operatorname{Arccosh}z=\pm\operatorname{% arccosh}z+2k\pi i,}}
    0 references
    DLMF id
    DLMF:4.37.E30
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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.m2ahdec
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    Q11246
    Defining formula
    arccosh ⁡ z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m9ahdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ajdec
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    general inverse hyperbolic cosine function
    Defining formula
    Arccosh ⁡ z multivalued-hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccosh}\NVar{z}}}
    xml-id
    C4.S37.E2.m2abdec
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