DLMF:4.38.E1 (Q1951)

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DLMF:4.38.E1
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    arcsinh z = z - 1 2 z 3 3 + 1 3 2 4 z 5 5 - 1 3 5 2 4 6 z 7 7 + , hyperbolic-inverse-sine 𝑧 𝑧 1 2 superscript 𝑧 3 3 1 3 2 4 superscript 𝑧 5 5 1 3 5 2 4 6 superscript 𝑧 7 7 {\displaystyle{\displaystyle\operatorname{arcsinh}z=z-\frac{1}{2}\frac{z^{3}}{% 3}+\frac{1\cdot 3}{2\cdot 4}\frac{z^{5}}{5}-\frac{1\cdot 3\cdot 5}{2\cdot 4% \cdot 6}\frac{z^{7}}{7}+\cdots,}}
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    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
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