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DLMF:4.38.E5 - MaRDI portal

DLMF:4.38.E5 (Q2391)

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DLMF:4.38.E5
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    Statements

    DLMF defining formula
    arctanh ⁡ z = z + z 3 3 + z 5 5 + z 7 7 + ⋯ , hyperbolic-inverse-tangent 𝑧 𝑧 superscript 𝑧 3 3 superscript 𝑧 5 5 superscript 𝑧 7 7 ⋯ {\displaystyle{\displaystyle\operatorname{arctanh}z=z+\frac{z^{3}}{3}+\frac{z^% {5}}{5}+\frac{z^{7}}{7}+\cdots,}}
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    constraint
    | z | ≤ 1 𝑧 1 {\displaystyle{\displaystyle\left|z\right|\leq 1}}
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    | z | ≤ 1 𝑧 1 {\displaystyle{\displaystyle\left|z\right|\leq 1}}
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    z ≠ ± 1 𝑧 plus-or-minus 1 {\displaystyle{\displaystyle z\neq\pm 1}}
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    Symbols used
    Q11219
    DLMF defining formula
    arctanh ⁡ z hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{arctanh}\NVar{z}}}
    xml-id
    C4.S37.SS2.p1.m10adec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1ddec
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    Identifiers

     
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