The Exponential Integral and Variants
Computes the exponential integral Ei(x) for real values, as well as exp(-x) * Ei(x) and E_1(x) and their derivatives (up to the 3rd derivative).
expint(x, deriv = 0) expexpint(x, deriv = 0) expint.E1(x, deriv = 0)
x |
Numeric. Ideally a vector of positive reals. |
deriv |
Integer. Either 0, 1, 2 or 3. |
The exponential integral Ei(x) function is the integral of exp(t) / t from 0 to x, for positive real x. The function E_1(x) is the integral of exp(-t) / t from x to infinity, for positive real x.
Function expint(x, deriv = n) returns the
nth derivative of Ei(x) (up to the 3rd),
function expexpint(x, deriv = n) returns the
nth derivative of
exp(-x) * Ei(x) (up to the 3rd),
function expint.E1(x, deriv = n) returns the nth
derivative of E_1(x) (up to the 3rd).
These functions have not been tested thoroughly.
T. W. Yee has simply written a small wrapper function to call the NETLIB FORTRAN code. Xiangjie Xue modified the functions to calculate derivatives. Higher derivatives can actually be calculated—please let me know if you need it.
## Not run:
par(mfrow = c(2, 2))
curve(expint, 0.01, 2, xlim = c(0, 2), ylim = c(-3, 5),
las = 1, col = "orange")
abline(v = (-3):5, h = (-4):5, lwd = 2, lty = "dotted", col = "gray")
abline(h = 0, v = 0, lty = "dashed", col = "blue")
curve(expexpint, 0.01, 2, xlim = c(0, 2), ylim = c(-3, 2),
las = 1, col = "orange")
abline(v = (-3):2, h = (-4):5, lwd = 2, lty = "dotted", col = "gray")
abline(h = 0, v = 0, lty = "dashed", col = "blue")
curve(expint.E1, 0.01, 2, xlim = c(0, 2), ylim = c(0, 5),
las = 1, col = "orange")
abline(v = (-3):2, h = (-4):5, lwd = 2, lty = "dotted", col = "gray")
abline(h = 0, v = 0, lty = "dashed", col = "blue")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.