back to table · edit · history · where entries came from · files
Formulas: formula-generating-function: $\left(\frac{t}{1-e^{-t}}\right)^{x+1} =\sum_{k=0}^{\infty}S_k(x)\frac{t^k}{k!}$.- formula-norlund: $S_k(x)=B_k^{(x+1)}(x+1)$, where the generalized Bernoulli polynomials+ formula-norlund: $S_k(x)=B_k^{(x+1)}(x+1)$, where the Noerlund polynomials $B_k^{(a)}(z)$ are defined by $\left(\frac{t}{e^t-1}\right)^a e^{zt} =\sum_{k=0}^{\infty}B_k^{(a)}(z)\frac{t^k}{k!}$- CITE{Wiki}.+ CITE{Wiki}. At $a=1$, these are the HREF{Bernoulli_polynomials}[Bernoulli polynomials]. formula-special-values: $S_k(-1)=\delta_{k,0}$, $S_k(0)=(-1)^kB_k$, and $S_k(k)=k!$. formula-first-kind: If $m$ and $k$ are integers with $m\geq k\geq0$, then $S_k(m)=\frac{(-1)^k}{\binom{m}{k}}s(m+1,m+1-k)$,
Sign in to restore an earlier version.
