DLMF:4.38.E17 (Q1967)

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DLMF:4.38.E17
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    Statements

    Defining formula
    Arctanh ⁡ u ± Arctanh ⁡ v = Arctanh ⁡ ( u ± v 1 ± u ⁢ v ) , plus-or-minus multivalued-hyperbolic-inverse-tangent 𝑢 multivalued-hyperbolic-inverse-tangent 𝑣 multivalued-hyperbolic-inverse-tangent plus-or-minus 𝑢 𝑣 plus-or-minus 1 𝑢 𝑣 {\displaystyle{\displaystyle\operatorname{Arctanh}u\pm\operatorname{Arctanh}v=% \operatorname{Arctanh}\left(\frac{u\pm v}{1\pm uv}\right),}}
    0 references
    DLMF id
    DLMF:4.38.E17
    0 references
    Symbols used
    general inverse hyperbolic tangent function
    Defining formula
    Arctanh ⁡ z multivalued-hyperbolic-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctanh}\NVar{z}}}
    xml-id
    C4.S37.E3.m2adec
    0 references
     
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