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Formula:8122

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Digital Library of Mathematical Functions ID 24.4.E16

E 2 ⁢ n = 1 2 ⁢ n + 1 - ∑ k = 1 n ( 2 ⁢ n 2 ⁢ k - 1 ) ⁢ 2 2 ⁢ k ⁢ ( 2 2 ⁢ k - 1 - 1 ) ⁢ B 2 ⁢ k k , Euler-number-E 2 𝑛 1 2 𝑛 1 superscript subscript 𝑘 1 𝑛 binomial 2 𝑛 2 𝑘 1 superscript 2 2 𝑘 superscript 2 2 𝑘 1 1 Bernoulli-number-B 2 𝑘 𝑘 {\displaystyle{\displaystyle E_{2n}=\frac{1}{2n+1}-\sum_{k=1}^{n}{2n\choose 2k% -1}\frac{2^{2k}(2^{2k-1}-1)B_{2k}}{k},}}


Constraint(s)

Symbols List

  • B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}} :
  • E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}} :
  • ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}} :
  • k 𝑘 {\displaystyle{\displaystyle k}} : integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
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This page was last edited on 28 January 2024, at 10:02.
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