Lambert W Function and Its Derivatives

Functions to compute the Lambert W function and its derivatives for the principal branch (\(W_0\)) and the branch -1 (\(W_{-1}\)).

Usage

lambert_w0(z)

lambert_wm1(z)

lambert_w0_prime(z)

lambert_wm1_prime(z)

Arguments

z

Argument of the Lambert W function

Value

A single numeric value with the computed Lambert W function or its derivative.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Lambert W Function (Principal Branch)
lambert_w0(0.3)
#> [1] 0.2367553
# Lambert W Function (Branch -1)
lambert_wm1(-0.3)
#> [1] -1.781337
# Derivative of the Lambert W Function (Principal Branch)
lambert_w0_prime(0.3)
#> [1] 0.6381087
# Derivative of the Lambert W Function (Branch -1)
lambert_wm1_prime(-0.3)
#> [1] -7.599525