# Fungrim entry: 588889

Table of $B_{n}\!\left(x\right)$ for $0 \le n \le 10$
$n$ $B_{n}\!\left(x\right)$
01
1$x - \frac{1}{2}$
2${x}^{2} - x + \frac{1}{6}$
3${x}^{3} - \frac{3}{2} {x}^{2} + \frac{1}{2} x$
4${x}^{4} - 2 {x}^{3} + {x}^{2} - \frac{1}{30}$
5${x}^{5} - \frac{5}{2} {x}^{4} + \frac{5}{3} {x}^{3} - \frac{1}{6} x$
6${x}^{6} - 3 {x}^{5} + \frac{5}{2} {x}^{4} - \frac{1}{2} {x}^{2} + \frac{1}{42}$
7${x}^{7} - \frac{7}{2} {x}^{6} + \frac{7}{2} {x}^{5} - \frac{7}{6} {x}^{3} + \frac{1}{6} x$
8${x}^{8} - 4 {x}^{7} + \frac{14}{3} {x}^{6} - \frac{7}{3} {x}^{4} + \frac{2}{3} {x}^{2} - \frac{1}{30}$
9${x}^{9} - \frac{9}{2} {x}^{8} + 6 {x}^{7} - \frac{21}{5} {x}^{5} + 2 {x}^{3} - \frac{3}{10} x$
10${x}^{10} - 5 {x}^{9} + \frac{15}{2} {x}^{8} - 7 {x}^{6} + 5 {x}^{4} - \frac{3}{2} {x}^{2} + \frac{5}{66}$
Table data: $\left(n, p\right)$ such that $B_{n}\!\left(x\right) = p$
Assumptions:$x \in \mathbb{C}$
TeX:
x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomial$B_{n}\!\left(z\right)$ Bernoulli polynomial
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("588889"),
Description("Table of", BernoulliPolynomial(n, x), "for", LessEqual(0, n, 10)),
Assumptions(Element(x, CC)))