Chebyshev: Chebyshev Polynomials

In ArcadeAntics/polynomial:

Usage

Chebyshev1(n)
Chebyshev2(n)
ChebyshevT(n)
ChebyshevU(n)

Arguments

n	non-negative integer; order of the Chebyshev polynomial

Examples

par(mar = c(4.5, 4.5, 1.7, 4.5), xpd = FALSE)
plot(
    xlim = c(-1, 1), ylim = c(-1, 1),
    panel.first = grid(col = "gray69"),
    x = NA_real_, y = NA_real_,
    xlab = "x", ylab = ~T ~ ""[n](x), main = "Chebyshev polynomials of the first kind"
)
n <- 0:4
col <- c("#0072B2", "#E69F00", "#009E73", "#D55E00", "#56B4E9")
for (i in seq_along(n)) {
    x <- as.polynomial(Chebyshev1(n[i]))
    lines(x, col = col[i], n = 1001, lwd = 2)
}
par(xpd = TRUE)
legend(x = par("usr")[2L], y = par("usr")[4L],
    legend = paste0("n = ", n),
    fill = col,
    bty = "n")





par(mar = c(4.5, 4.5, 1.7, 4.5), xpd = FALSE)
plot(
    xlim = c(-1, 1), ylim = c(-4, 5),
    panel.first = grid(col = "gray69"),
    x = NA_real_, y = NA_real_,
    xlab = "x", ylab = ~U ~ ""[n](x), main = "Chebyshev polynomials of the second kind"
)
n <- 0:4
col <- c("#0072B2", "#E69F00", "#009E73", "#D55E00", "#56B4E9")
for (i in seq_along(n)) {
    x <- as.polynomial(Chebyshev2(n[i]))
    lines(x, col = col[i], n = 1001, lwd = 2)
}
par(xpd = TRUE)
legend(x = par("usr")[2L], y = par("usr")[4L],
    legend = paste0("n = ", n),
    fill = col,
    bty = "n")

ArcadeAntics/polynomial documentation built on Jan. 19, 2021, 12:32 a.m.