DLMF:4.37.E29 (Q1948)

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DLMF:4.37.E29
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    Statements

    Defining formula
    w = Arcsinh ⁡ z = ( - 1 ) k ⁢ arcsinh ⁡ z + k ⁢ π ⁢ i , 𝑤 multivalued-hyperbolic-inverse-sine 𝑧 superscript 1 𝑘 hyperbolic-inverse-sine 𝑧 𝑘 𝜋 𝑖 {\displaystyle{\displaystyle w=\operatorname{Arcsinh}z=(-1)^{k}\operatorname{% arcsinh}z+k\pi i,}}
    0 references
    DLMF id
    DLMF:4.37.E29
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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.m2agdec
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    Q11247
    Defining formula
    arcsinh ⁡ z hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{arcsinh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m8afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
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    general inverse hyperbolic sine function
    Defining formula
    Arcsinh ⁡ z multivalued-hyperbolic-inverse-sine 𝑧 {\displaystyle{\displaystyle\operatorname{Arcsinh}\NVar{z}}}
    xml-id
    C4.S37.E1.m2abdec
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    Q11219
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C4.S1.XMD1.m1dec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1wdec
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