DLMF:4.24.E4 (Q1798)

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DLMF:4.24.E4
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    Statements

    Defining formula
    arctan ⁡ z = ± π 2 - 1 z + 1 3 ⁢ z 3 - 1 5 ⁢ z 5 + ⋯ , 𝑧 plus-or-minus 𝜋 2 1 𝑧 1 3 superscript 𝑧 3 1 5 superscript 𝑧 5 ⋯ {\displaystyle{\displaystyle\operatorname{arctan}z=\pm\frac{\pi}{2}-\frac{1}{z% }+\frac{1}{3z^{3}}-\frac{1}{5z^{5}}+\cdots,}}
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    DLMF id
    DLMF:4.24.E4
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    constraint
    ℜ ⁡ z ≷ 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}}
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    ℜ ⁡ z ≷ 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}}
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    | z | ≥ 1 𝑧 1 {\displaystyle{\displaystyle|z|\geq 1}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7aadec
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    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
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    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1cdec
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