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25 March 2024
24 March 2024
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N 16:12 | Integral Representation of Bernoulli Number 3 changes history +2,205 [Prime.mover; Robkahn131 (2×)] | |||
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16:12 (cur | prev) −10 Prime.mover talk contribs | |||
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16:01 (cur | prev) −89 Robkahn131 talk contribs | |||
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16:00 (cur | prev) +2,304 Robkahn131 talk contribs (Created page with "== Theorem == <onlyinclude> Bernoulli numbers can be expressed in integral form as follows: :$\ds \size {B_{2 n} } = 4 n \int_0^\infty \frac {t^{2 n - 1} } {e^t - 1} \rd t$ where: :$B_n$ are the Bernoulli numbers :$n$ is a positive integer. </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \map \zeta s \map \Gamma s | r = \int_0^\infty \frac {t^{s - 1} } {e^t -...") |