Update the lambert_w dependency to version 2

Cargo.toml

@@ -17,7 +17,7 @@ readme = "README.md"
 rustdoc-args = ["--html-in-header", "katex-header.html", "--cfg", "docsrs"]
 
 [dependencies]
-lambert_w = { version = "1.2.34", default-features = false, features = ["std"] }
+lambert_w = { version = "2.0.1", default-features = false, features = ["std"] }
 num-complex = { version = "0.4.6" }
 
 [dev-dependencies]

src/lib.rs

@@ -2,7 +2,24 @@
 // Import from other crates
 // =============================================================================
 // Lambert W functions
-pub use lambert_w::{lambert_w, lambert_w0, lambert_wm1, sp_lambert_w0, sp_lambert_wm1};
+pub use lambert_w::{lambert_w0, lambert_wm1, sp_lambert_w0, sp_lambert_wm1};
+use lambert_w::lambert_w as complex_lambert_w;
+
+// Re-export the complex Lambert W function as the version of `lambert_w` from version 2 of the crate takes an error tolerance,
+// which we set to floating point epsilon to match the API and performance of version 1.
+/// Branch k of the complex valued Lambert W function computed on 64-bit floats with Halley's method.
+/// The return value is a tuple where the first element is the real part and the second element is the imaginary part.
+///
+/// The function iterates until the current and previous iterations are within floating point epsilon, or it has iterated a maximum number of times.
+///
+/// This function may be slightly less accurate close to the branch cut at -1/e, as well as close to zero on branches other than k=0.
+///
+/// If you know you want the principal or secondary branches where they are real-valued, take a look at the [`lambert_w0`] or [`lambert_wm1`] functions instead. They can be up to two orders of magnitude faster.
+// We inline this function since it's just a trivial wrapper.
+#[inline]
+pub fn lambert_w(k: i32, z_re: f64, z_im: f64) -> (f64, f64) {
+    complex_lambert_w(k, z_re, z_im, f64::EPSILON)
+}
 
 // =============================================================================
 // Export funcionts