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Fungrim entry: 85e42e

Table of Tn ⁣(x)T_{n}\!\left(x\right) for 0n150 \le n \le 15
nn Tn ⁣(x)T_{n}\!\left(x\right)
01
1xx
22x212 {x}^{2} - 1
34x33x4 {x}^{3} - 3 x
48x48x2+18 {x}^{4} - 8 {x}^{2} + 1
516x520x3+5x16 {x}^{5} - 20 {x}^{3} + 5 x
632x648x4+18x2132 {x}^{6} - 48 {x}^{4} + 18 {x}^{2} - 1
764x7112x5+56x37x64 {x}^{7} - 112 {x}^{5} + 56 {x}^{3} - 7 x
8128x8256x6+160x432x2+1128 {x}^{8} - 256 {x}^{6} + 160 {x}^{4} - 32 {x}^{2} + 1
9256x9576x7+432x5120x3+9x256 {x}^{9} - 576 {x}^{7} + 432 {x}^{5} - 120 {x}^{3} + 9 x
10512x101280x8+1120x6400x4+50x21512 {x}^{10} - 1280 {x}^{8} + 1120 {x}^{6} - 400 {x}^{4} + 50 {x}^{2} - 1
111024x112816x9+2816x71232x5+220x311x1024 {x}^{11} - 2816 {x}^{9} + 2816 {x}^{7} - 1232 {x}^{5} + 220 {x}^{3} - 11 x
122048x126144x10+6912x83584x6+840x472x2+12048 {x}^{12} - 6144 {x}^{10} + 6912 {x}^{8} - 3584 {x}^{6} + 840 {x}^{4} - 72 {x}^{2} + 1
134096x1313312x11+16640x99984x7+2912x5364x3+13x4096 {x}^{13} - 13312 {x}^{11} + 16640 {x}^{9} - 9984 {x}^{7} + 2912 {x}^{5} - 364 {x}^{3} + 13 x
148192x1428672x12+39424x1026880x8+9408x61568x4+98x218192 {x}^{14} - 28672 {x}^{12} + 39424 {x}^{10} - 26880 {x}^{8} + 9408 {x}^{6} - 1568 {x}^{4} + 98 {x}^{2} - 1
1516384x1561440x13+92160x1170400x9+28800x76048x5+560x315x16384 {x}^{15} - 61440 {x}^{13} + 92160 {x}^{11} - 70400 {x}^{9} + 28800 {x}^{7} - 6048 {x}^{5} + 560 {x}^{3} - 15 x
Table data: (n,p)\left(n, p\right) such that Tn ⁣(x)=pT_{n}\!\left(x\right) = p
Assumptions:xCx \in \mathbb{C}
TeX:
x \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("85e42e"),
    Description("Table of", ChebyshevT(n, x), "for", LessEqual(0, n, 15)),
    Table(TableRelation(Tuple(n, p), Equal(ChebyshevT(n, x), p)), TableHeadings(n, ChebyshevT(n, x)), TableSplit(1), List(Tuple(0, 1), Tuple(1, x), Tuple(2, Sub(Mul(2, Pow(x, 2)), 1)), Tuple(3, Sub(Mul(4, Pow(x, 3)), Mul(3, x))), Tuple(4, Add(Sub(Mul(8, Pow(x, 4)), Mul(8, Pow(x, 2))), 1)), Tuple(5, Add(Sub(Mul(16, Pow(x, 5)), Mul(20, Pow(x, 3))), Mul(5, x))), Tuple(6, Sub(Add(Sub(Mul(32, Pow(x, 6)), Mul(48, Pow(x, 4))), Mul(18, Pow(x, 2))), 1)), Tuple(7, Sub(Add(Sub(Mul(64, Pow(x, 7)), Mul(112, Pow(x, 5))), Mul(56, Pow(x, 3))), Mul(7, x))), Tuple(8, Add(Sub(Add(Sub(Mul(128, Pow(x, 8)), Mul(256, Pow(x, 6))), Mul(160, Pow(x, 4))), Mul(32, Pow(x, 2))), 1)), Tuple(9, Add(Sub(Add(Sub(Mul(256, Pow(x, 9)), Mul(576, Pow(x, 7))), Mul(432, Pow(x, 5))), Mul(120, Pow(x, 3))), Mul(9, x))), Tuple(10, Sub(Add(Sub(Add(Sub(Mul(512, Pow(x, 10)), Mul(1280, Pow(x, 8))), Mul(1120, Pow(x, 6))), Mul(400, Pow(x, 4))), Mul(50, Pow(x, 2))), 1)), Tuple(11, Sub(Add(Sub(Add(Sub(Mul(1024, Pow(x, 11)), Mul(2816, Pow(x, 9))), Mul(2816, Pow(x, 7))), Mul(1232, Pow(x, 5))), Mul(220, Pow(x, 3))), Mul(11, x))), Tuple(12, Add(Sub(Add(Sub(Add(Sub(Mul(2048, Pow(x, 12)), Mul(6144, Pow(x, 10))), Mul(6912, Pow(x, 8))), Mul(3584, Pow(x, 6))), Mul(840, Pow(x, 4))), Mul(72, Pow(x, 2))), 1)), Tuple(13, Add(Sub(Add(Sub(Add(Sub(Mul(4096, Pow(x, 13)), Mul(13312, Pow(x, 11))), Mul(16640, Pow(x, 9))), Mul(9984, Pow(x, 7))), Mul(2912, Pow(x, 5))), Mul(364, Pow(x, 3))), Mul(13, x))), Tuple(14, Sub(Add(Sub(Add(Sub(Add(Sub(Mul(8192, Pow(x, 14)), Mul(28672, Pow(x, 12))), Mul(39424, Pow(x, 10))), Mul(26880, Pow(x, 8))), Mul(9408, Pow(x, 6))), Mul(1568, Pow(x, 4))), Mul(98, Pow(x, 2))), 1)), Tuple(15, Sub(Add(Sub(Add(Sub(Add(Sub(Mul(16384, Pow(x, 15)), Mul(61440, Pow(x, 13))), Mul(92160, Pow(x, 11))), Mul(70400, Pow(x, 9))), Mul(28800, Pow(x, 7))), Mul(6048, Pow(x, 5))), Mul(560, Pow(x, 3))), Mul(15, x))))),
    Variables(x),
    Assumptions(Element(x, CC)))

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2019-09-22 15:43:45.410764 UTC