expint {VGAM} | R Documentation |
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.
http://www.netlib.org/specfun/ei.
## 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)