Asymptotic Formula for Bernoulli Numbers/Also presented as

Asymptotic Formula for Bernoulli Numbers: Also presented as

Asymptotic Formula for Bernoulli Numbers can also be presented in the form:

$B_{2 n} \sim \paren {-1}^{n + 1} 4 n^{2 n} \paren {\pi e}^{-2 n} \sqrt {\pi n}$

The following can also be seen:

${B_n}^* \sim 4 n^{2 n} \paren {\pi e}^{-2 n} \sqrt {\pi n}$

where ${B_n}^*$ denotes the archaic form of the Bernoulli numbers.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 21$: Asymptotic Formula for Bernoulli Numbers: $21.12$
• 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 23$: Bernoulli and Euler Numbers: Asymptotic Formula for Bernoulli Numbers: $23.12.$