• Bernoulli number
• Bernoulli numbers

Bernoulli number (suomeksi)

Määritelmät:

• (lb, en, mathematics) One of a sequence of coefficients of a power series which allow one to (relatively speedily) compute the error of a partial sum of some series (with respect to the limit of that series). In particular, if $\backslash pi^2\; /\; 6$ is expressed as the series $\backslash Sigma\_\{n=1\}^\backslash infty\; \{1\; /\; n^2\}$ then the partial sum $S\_n\; =\; \backslash Sigma\_\{k=1\}^n\; 1/k^2$ differs from the limit $\backslash pi^2\; /\; 6$ by an error $E\_n$ which is precisely expressible by the series $B\_0\; /\; n\; +\; B\_1\; /\; n^2\; +\; B\_2\; /\; n^3\; +\; B\_3\; /\; n^4\; +\; ...$, where the sequence $B\_0,\; B\_1,\; B\_2,\; B\_3,...$ is the sequence of ''Bernoulli numbers''.