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Fungrim entry: 9789ee

T2n+1 ⁣(sin(x))=(1)nsin ⁣((2n+1)x)T_{2 n + 1}\!\left(\sin(x)\right) = {\left(-1\right)}^{n} \sin\!\left(\left(2 n + 1\right) x\right)
Assumptions:nZ  and  xCn \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
T_{2 n + 1}\!\left(\sin(x)\right) = {\left(-1\right)}^{n} \sin\!\left(\left(2 n + 1\right) x\right)

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; x \in \mathbb{C}
Fungrim symbol Notation Short description
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
Sinsin(z)\sin(z) Sine
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(ChebyshevT(Add(Mul(2, n), 1), Sin(x)), Mul(Pow(-1, n), Sin(Mul(Add(Mul(2, n), 1), x))))),
    Variables(n, x),
    Assumptions(And(Element(n, ZZ), Element(x, CC))))

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2021-03-15 19:12:00.328586 UTC