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Fungrim entry: 9789ee

T2n+1 ⁣(sin ⁣(x))=(1)nsin ⁣((2n+1)x)T_{2 n + 1}\!\left(\sin\!\left(x\right)\right) = {\left(-1\right)}^{n} \sin\!\left(\left(2 n + 1\right) x\right)
Assumptions:nZandxCn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
T_{2 n + 1}\!\left(\sin\!\left(x\right)\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}
Definitions:
Fungrim symbol Notation Short description
ChebyshevTTn ⁣(x)T_{n}\!\left(x\right) Chebyshev polynomial of the first kind
Sinsin ⁣(z)\sin\!\left(z\right) Sine
Powab{a}^{b} Power
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("9789ee"),
    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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2019-08-25 15:30:03.056001 UTC