gsignal (version 0.3-1)

cheb: Chebyshev polynomials

Description

Return the value of the Chebyshev polynomial at specific points.

Usage

cheb(n, x)

Arguments

n

Order of the polynomial, specified as a positive integer.

x

Point or points at which to calculate the Chebyshev polynomial

Value

Polynomial of order x, evaluated at point(s) x.

Details

The Chebyshev polynomials are defined by the equations:

  Tn(x) = cos(n . acos(x),    |x|<= 1
  Tn(x) = cosh(n . acosh(x),  |x|> 1

If x is a vector, the output is a vector of the same size, where each element is calculated as \(y(i) = Tn(x(i))\).

Examples

# NOT RUN {
cp <- cheb(5, 1)
cp <- cheb(5, c(2,3))

# }