DLMF:24.7.E3 (Q7479): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
test:

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

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1abdec

Revision as of 00:33, 2 January 2020

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DLMF:24.7.E3
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    Statements

    B 2 n = ( - 1 ) n + 1 π 1 - 2 1 - 2 n 0 t 2 n sech 2 ( π t ) d t , Bernoulli-number-B 2 𝑛 superscript 1 𝑛 1 𝜋 1 superscript 2 1 2 𝑛 superscript subscript 0 superscript 𝑡 2 𝑛 2 𝜋 𝑡 𝑡 {\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{% \infty}t^{2n}{\operatorname{sech}^{2}}\left(\pi t\right)\mathrm{d}t,}}
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    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1abdec
    0 references