Fungrim home page

# 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

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

2021-03-15 19:12:00.328586 UTC