DLMF:4.38.E3 (Q1953)

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DLMF:4.38.E3
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    Statements

    test
    arccosh ⁡ z = ln ⁡ ( 2 ⁢ z ) - 1 2 ⁢ 1 2 ⁢ z 2 - 1 ⋅ 3 2 ⋅ 4 ⁢ 1 4 ⁢ z 4 - 1 ⋅ 3 ⋅ 5 2 ⋅ 4 ⋅ 6 ⁢ 1 6 ⁢ z 6 - ⋯ , hyperbolic-inverse-cosine 𝑧 2 𝑧 1 2 1 2 superscript 𝑧 2 ⋅ 1 3 ⋅ 2 4 1 4 superscript 𝑧 4 ⋅ 1 3 5 ⋅ 2 4 6 1 6 superscript 𝑧 6 ⋯ {\displaystyle{\displaystyle\operatorname{arccosh}z=\ln\left(2z\right)-\frac{1% }{2}\frac{1}{2z^{2}}-\frac{1\cdot 3}{2\cdot 4}\frac{1}{4z^{4}}-\frac{1\cdot 3% \cdot 5}{2\cdot 4\cdot 6}\frac{1}{6z^{6}}-\cdots,}}
    0 references
    DLMF id
    DLMF:4.38.E3
    0 references
    constraint
    | z | > 1 𝑧 1 {\displaystyle{\displaystyle|z|>1}}
    0 references
    Symbols used
    Q11246
    test
    arccosh ⁡ z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m9adec
    0 references
     
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