DLMF:4.19.E8 (Q1687): Difference between revisions

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Property / constraint
 

| z | < 1 2 π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}

|z|<\frac{1}{2}\pi
Property / constraint: | z | < 1 2 π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}} / rank
 
Normal rank

Revision as of 16:00, 30 December 2019

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DLMF:4.19.E8
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    Statements

    ln ( cos z ) = n = 1 ( - 1 ) n 2 2 n - 1 ( 2 2 n - 1 ) B 2 n n ( 2 n ) ! z 2 n , 𝑧 superscript subscript 𝑛 1 superscript 1 𝑛 superscript 2 2 𝑛 1 superscript 2 2 𝑛 1 Bernoulli-number-B 2 𝑛 𝑛 2 𝑛 superscript 𝑧 2 𝑛 {\displaystyle{\displaystyle\ln\left(\cos z\right)=\sum_{n=1}^{\infty}\frac{(-% 1)^{n}2^{2n-1}(2^{2n}-1)B_{2n}}{n(2n)!}z^{2n},}}
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    | z | < 1 2 π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}
    0 references