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Fungrim entry: 588889

Table of Bn ⁣(x)B_{n}\!\left(x\right) for 0n100 \le n \le 10
nn Bn ⁣(x)B_{n}\!\left(x\right)
01
1x12x - \frac{1}{2}
2x2x+16{x}^{2} - x + \frac{1}{6}
3x332x2+12x{x}^{3} - \frac{3}{2} {x}^{2} + \frac{1}{2} x
4x42x3+x2130{x}^{4} - 2 {x}^{3} + {x}^{2} - \frac{1}{30}
5x552x4+53x316x{x}^{5} - \frac{5}{2} {x}^{4} + \frac{5}{3} {x}^{3} - \frac{1}{6} x
6x63x5+52x412x2+142{x}^{6} - 3 {x}^{5} + \frac{5}{2} {x}^{4} - \frac{1}{2} {x}^{2} + \frac{1}{42}
7x772x6+72x576x3+16x{x}^{7} - \frac{7}{2} {x}^{6} + \frac{7}{2} {x}^{5} - \frac{7}{6} {x}^{3} + \frac{1}{6} x
8x84x7+143x673x4+23x2130{x}^{8} - 4 {x}^{7} + \frac{14}{3} {x}^{6} - \frac{7}{3} {x}^{4} + \frac{2}{3} {x}^{2} - \frac{1}{30}
9x992x8+6x7215x5+2x3310x{x}^{9} - \frac{9}{2} {x}^{8} + 6 {x}^{7} - \frac{21}{5} {x}^{5} + 2 {x}^{3} - \frac{3}{10} x
10x105x9+152x87x6+5x432x2+566{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: (n,p)\left(n, p\right) such that Bn ⁣(x)=pB_{n}\!\left(x\right) = p
Assumptions:xCx \in \mathbb{C}
TeX:
x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
BernoulliPolynomialBn ⁣(z)B_{n}\!\left(z\right) Bernoulli polynomial
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("588889"),
    Description("Table of", BernoulliPolynomial(n, x), "for", LessEqual(0, n, 10)),
    Table(TableRelation(Tuple(n, p), Equal(BernoulliPolynomial(n, x), p)), TableHeadings(n, BernoulliPolynomial(n, x)), TableSplit(1), List(Tuple(0, 1), Tuple(1, Sub(x, Div(1, 2))), Tuple(2, Add(Sub(Pow(x, 2), x), Div(1, 6))), Tuple(3, Add(Sub(Pow(x, 3), Mul(Div(3, 2), Pow(x, 2))), Mul(Div(1, 2), x))), Tuple(4, Sub(Add(Sub(Pow(x, 4), Mul(2, Pow(x, 3))), Pow(x, 2)), Div(1, 30))), Tuple(5, Sub(Add(Sub(Pow(x, 5), Mul(Div(5, 2), Pow(x, 4))), Mul(Div(5, 3), Pow(x, 3))), Mul(Div(1, 6), x))), Tuple(6, Add(Sub(Add(Sub(Pow(x, 6), Mul(3, Pow(x, 5))), Mul(Div(5, 2), Pow(x, 4))), Mul(Div(1, 2), Pow(x, 2))), Div(1, 42))), Tuple(7, Add(Sub(Add(Sub(Pow(x, 7), Mul(Div(7, 2), Pow(x, 6))), Mul(Div(7, 2), Pow(x, 5))), Mul(Div(7, 6), Pow(x, 3))), Mul(Div(1, 6), x))), Tuple(8, Sub(Add(Sub(Add(Sub(Pow(x, 8), Mul(4, Pow(x, 7))), Mul(Div(14, 3), Pow(x, 6))), Mul(Div(7, 3), Pow(x, 4))), Mul(Div(2, 3), Pow(x, 2))), Div(1, 30))), Tuple(9, Sub(Add(Sub(Add(Sub(Pow(x, 9), Mul(Div(9, 2), Pow(x, 8))), Mul(6, Pow(x, 7))), Mul(Div(21, 5), Pow(x, 5))), Mul(2, Pow(x, 3))), Mul(Div(3, 10), x))), Tuple(10, Add(Sub(Add(Sub(Add(Sub(Pow(x, 10), Mul(5, Pow(x, 9))), Mul(Div(15, 2), Pow(x, 8))), Mul(7, Pow(x, 6))), Mul(5, Pow(x, 4))), Mul(Div(3, 2), Pow(x, 2))), Div(5, 66))))),
    Variables(x),
    Assumptions(Element(x, CC)))

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2019-10-05 13:11:19.856591 UTC