DLMF:4.19.E6 (Q1685)

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DLMF:4.19.E6
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    Statements

    Defining formula
    cot ⁡ z = 1 z - z 3 - z 3 45 - 2 945 ⁢ z 5 - ⋯ - ( - 1 ) n - 1 ⁢ 2 2 ⁢ n ⁢ B 2 ⁢ n ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n - 1 - ⋯ , 𝑧 1 𝑧 𝑧 3 superscript 𝑧 3 45 2 945 superscript 𝑧 5 ⋯ superscript 1 𝑛 1 superscript 2 2 𝑛 Bernoulli-number-B 2 𝑛 2 𝑛 superscript 𝑧 2 𝑛 1 ⋯ {\displaystyle{\displaystyle\cot z=\frac{1}{z}-\frac{z}{3}-\frac{z^{3}}{45}-% \frac{2}{945}z^{5}-\cdots-\frac{(-1)^{n-1}2^{2n}B_{2n}}{(2n)!}z^{2n-1}-\cdots,}}
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    DLMF id
    DLMF:4.19.E6
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    constraint
    0 < | z | < π 0 𝑧 𝜋 {\displaystyle{\displaystyle 0<|z|<\pi}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1abdec
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