DLMF:4.24.E2 (Q1796)

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DLMF:4.24.E2
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    Statements

    Defining formula
    arccos ⁡ z = ( 2 ⁢ ( 1 - z ) ) 1 / 2 ⁢ ( 1 + ∑ n = 1 ∞ 1 ⋅ 3 ⋅ 5 ⁢ ⋯ ⁢ ( 2 ⁢ n - 1 ) 2 2 ⁢ n ⁢ ( 2 ⁢ n + 1 ) ⁢ n ! ⁢ ( 1 - z ) n ) , 𝑧 superscript 2 1 𝑧 1 2 1 superscript subscript 𝑛 1 ⋅ 1 3 5 ⋯ 2 𝑛 1 superscript 2 2 𝑛 2 𝑛 1 𝑛 superscript 1 𝑧 𝑛 {\displaystyle{\displaystyle\operatorname{arccos}z=(2(1-z))^{1/2}\*\left(1+% \sum_{n=1}^{\infty}\frac{1\cdot 3\cdot 5\cdots(2n-1)}{2^{2n}(2n+1)n!}(1-z)^{n}% \right),}}
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    DLMF id
    DLMF:4.24.E2
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    constraint
    | 1 - z | ≤ 2 1 𝑧 2 {\displaystyle{\displaystyle|1-z|\leq 2}}
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    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11208
    Defining formula
    arccos ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arccos}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m6adec
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