Exponential Integrals

Functions to compute various exponential integrals, including En and Ei.

Exponential Integral En:

Defined by the integral: $$E_n(z) = \int_1^\infty \frac{e^{-zt}}{t^n} dt$$

Exponential Integral Ei:

Defined by the integral: $$Ei(z) = -\int_{-z}^\infty \frac{e^{-t}}{t} dt$$

Usage

expint_en(n, z)

expint_ei(z)

Arguments

n

Order of the integral (for En), must be a non-negative integer

z

Argument of the integral (for En and Ei)

Value

A single numeric value with the computed exponential integral.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Exponential integral En with n = 1 and z = 2
expint_en(1, 2)
#> [1] 0.04890051
# Exponential integral Ei with z = 2
expint_ei(2)
#> [1] 4.954234