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• W2952202394 abstract "This article gives a direct formula for the computation of B(n) using the asymptotic formula $$B (n) approx 2 {frac {n!}{{pi}^{n}{2}^{n}}}$$ where n is even and $n >> 1$. This is simply based on the fact that $zeta (n)$ is very near 1 when n is large and since $B (n) = 2 {frac {zeta (n) n!}{{pi}^{n}{2}^{n}}}$ exactly. The formula chosen for the Zeta function is the one with prime numbers from the well-known Euler product for $zeta (n)$. This algorithm is far better than the recurrence formula for the Bernoulli numbers even if each B(n) is computed individually. The author could compute $B (750,000)$ in a few hours. The current record of computation is now (as of Feb. 2007) $B (5,000,000)$ a number of (the numerator) of 27332507 decimal digits is also based on that idea." @default.
• W2952202394 created "2019-06-27" @default.
• W2952202394 creator A5026210673 @default.
• W2952202394 creator A5080237955 @default.
• W2952202394 date "2007-02-11" @default.
• W2952202394 modified "2023-09-27" @default.
• W2952202394 title "An efficient algorithm for the computation of Bernoulli numbers" @default.
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