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Fungrim entry: ed5222

Tm ⁣(x)Tn ⁣(x)=Tm+n ⁣(x)+Tmn ⁣(x)2T_{m}\!\left(x\right) T_{n}\!\left(x\right) = \frac{T_{m + n}\!\left(x\right) + T_{\left|m - n\right|}\!\left(x\right)}{2}
Assumptions:mZandnZandxCm \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, x \in \mathbb{C}
TeX:
T_{m}\!\left(x\right) T_{n}\!\left(x\right) = \frac{T_{m + n}\!\left(x\right) + T_{\left|m - n\right|}\!\left(x\right)}{2}

m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, 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
Absz\left|z\right| Absolute value
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("ed5222"),
    Formula(Equal(Mul(ChebyshevT(m, x), ChebyshevT(n, x)), Div(Add(ChebyshevT(Add(m, n), x), ChebyshevT(Abs(Sub(m, n)), x)), 2))),
    Variables(m, n, x),
    Assumptions(And(Element(m, ZZ), Element(n, ZZ), Element(x, CC))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC