Fungrim entry: ed5222

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}

Assumptions:

m \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
`ChebyshevT`	$T_{n}\!\left(x\right)$	Chebyshev polynomial of the first kind
`Abs`	$\left\|z\right\|$	Absolute value
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	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))))

Topics using this entry

Chebyshev polynomials