DLMF:4.24.E17 (Q1811)

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DLMF:4.24.E17
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    Statements

    Defining formula
    Arctan ⁡ u ± Arccot ⁡ v = Arctan ⁡ ( u ⁢ v ± 1 v ∓ u ) = Arccot ⁡ ( v ∓ u u ⁢ v ± 1 ) . plus-or-minus multivalued-inverse-tangent 𝑢 multivalued-inverse-cotangent 𝑣 multivalued-inverse-tangent plus-or-minus 𝑢 𝑣 1 minus-or-plus 𝑣 𝑢 multivalued-inverse-cotangent minus-or-plus 𝑣 𝑢 plus-or-minus 𝑢 𝑣 1 {\displaystyle{\displaystyle\operatorname{Arctan}u\pm\operatorname{Arccot}v=% \operatorname{Arctan}\left(\frac{uv\pm 1}{v\mp u}\right)=\operatorname{Arccot}% \left(\frac{v\mp u}{uv\pm 1}\right).}}
    0 references
    DLMF id
    DLMF:4.24.E17
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    Symbols used
    general arccotangent function
    Defining formula
    Arccot ⁡ z multivalued-inverse-cotangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arccot}\NVar{z}}}
    xml-id
    C4.S23.E6.m2adec
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    general arctangent function
    Defining formula
    Arctan ⁡ z multivalued-inverse-tangent 𝑧 {\displaystyle{\displaystyle\operatorname{Arctan}\NVar{z}}}
    xml-id
    C4.S23.E3.m2aadec
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