require(graphics)
nus <- c(0:5, 10, 20)
x <- seq(0, 4, length.out = 501)
plot(x, x, ylim = c(0, 6), ylab = "", type = "n",
main = "Bessel Functions I_nu(x)")
for(nu in nus) lines(x, besselI(x, nu = nu), col = nu + 2)
legend(0, 6, legend = paste("nu=", nus), col = nus + 2, lwd = 1)
x <- seq(0, 40, length.out = 801); yl <- c(-.8, .8)
plot(x, x, ylim = yl, ylab = "", type = "n",
main = "Bessel Functions J_nu(x)")
for(nu in nus) lines(x, besselJ(x, nu = nu), col = nu + 2)
legend(32, -.18, legend = paste("nu=", nus), col = nus + 2, lwd = 1)
## Negative nu's :
xx <- 2:7
nu <- seq(-10, 9, length.out = 2001)
op <- par(lab = c(16, 5, 7))
matplot(nu, t(outer(xx, nu, besselI)), type = "l", ylim = c(-50, 200),
main = expression(paste("Bessel ", I[nu](x), " for fixed ", x,
", as ", f(nu))),
xlab = expression(nu))
abline(v = 0, col = "light gray", lty = 3)
legend(5, 200, legend = paste("x=", xx), col=seq(xx), lty=seq(xx))
par(op)
x0 <- 2^(-20:10)
plot(x0, x0^-8, log = "xy", ylab = "", type = "n",
main = "Bessel Functions J_nu(x) near 0\n log - log scale")
for(nu in sort(c(nus, nus+0.5)))
lines(x0, besselJ(x0, nu = nu), col = nu + 2)
legend(3, 1e50, legend = paste("nu=", paste(nus, nus+0.5, sep=",")),
col = nus + 2, lwd = 1)
plot(x0, x0^-8, log = "xy", ylab = "", type = "n",
main = "Bessel Functions K_nu(x) near 0\n log - log scale")
for(nu in sort(c(nus, nus+0.5)))
lines(x0, besselK(x0, nu = nu), col = nu + 2)
legend(3, 1e50, legend = paste("nu=", paste(nus, nus + 0.5, sep = ",")),
col = nus + 2, lwd = 1)
x <- x[x > 0]
plot(x, x, ylim = c(1e-18, 1e11), log = "y", ylab = "", type = "n",
main = "Bessel Functions K_nu(x)")
for(nu in nus) lines(x, besselK(x, nu = nu), col = nu + 2)
legend(0, 1e-5, legend=paste("nu=", nus), col = nus + 2, lwd = 1)
yl <- c(-1.6, .6)
plot(x, x, ylim = yl, ylab = "", type = "n",
main = "Bessel Functions Y_nu(x)")
for(nu in nus){
xx <- x[x > .6*nu]
lines(xx, besselY(xx, nu=nu), col = nu+2)
}
legend(25, -.5, legend = paste("nu=", nus), col = nus+2, lwd = 1)
## negative nu in bessel_Y -- was bogus for a long time
curve(besselY(x, -0.1), 0, 10, ylim = c(-3,1), ylab = "")
for(nu in c(seq(-0.2, -2, by = -0.1)))
curve(besselY(x, nu), add = TRUE)
title(expression(besselY(x, nu) * " " *
{nu == list(-0.1, -0.2, ..., -2)}))
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