DLMF:4.19.E7 (Q1686): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
Defining formula:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1acdec

Revision as of 18:22, 1 January 2020

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DLMF:4.19.E7
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    Statements

    Defining formula
    ln ⁡ ( sin ⁡ z z ) = ∑ n = 1 ∞ ( - 1 ) n ⁢ 2 2 ⁢ n - 1 ⁢ B 2 ⁢ n n ⁢ ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n , 𝑧 𝑧 superscript subscript 𝑛 1 superscript 1 𝑛 superscript 2 2 𝑛 1 Bernoulli-number-B 2 𝑛 𝑛 2 𝑛 superscript 𝑧 2 𝑛 {\displaystyle{\displaystyle\ln\left(\frac{\sin z}{z}\right)=\sum_{n=1}^{% \infty}\frac{(-1)^{n}2^{2n-1}B_{2n}}{n(2n)!}z^{2n},}}
    0 references
    DLMF id
    DLMF:4.19.E7
    0 references
    constraint
    | z | < π 𝑧 𝜋 {\displaystyle{\displaystyle|z|<\pi}}
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
     
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