Alternate representation of the Wright Omega Function The Wright Omega function, as introduced in Robert M. Corless and David J. Jeffrey's paper, is defined as:
$$\omega(z)=W_{\left\lceil\frac{\Im(z)-\pi}{2\pi}\right\rceil}(e^z)$$
Where the subscript $\left\lceil\frac{\Im(z)-\pi}{2\pi}\right\rceil$ is used as the unwinding number (related question), and $W(x)$ is the Lambert W function.
Programming languages like C++ do not offer the use of "unwinding numbers." However, it does allow for the compuation of functions like the Lambert W (through iterative convergence) and the variable $e$ (often through built-in functions). What other representations exist for the Wright Omega function? How can the Wright Omega function be expressed in a programmically-computable manner?

As a note:
Many other programming languages (like Maple, MATLAB, and the likes) do allow for the simple computation of the Wright Omega function, but in my case I am not using them. As demonstrated in the original author's paper, the Wright Omega function can be calculated in Maple in a few lines of code.
C++ does allow for the computation of other mathematical functions (many listed and easily usable in Boost's Special Functions C++ library, like gamma functions, factorials, beta functions, and such), but because of Wright Omega's unpopularity it is not one of the select few that is included in mathematical libraries like Boost and GMP.
 A: For numerical evaluation of the Wright $\omega$ function see the excellent paper by Lawrence, Corless, and Jeffrey: Algorithm 917: Complex Double-Precision Evaluation of the Wright $\omega$ Function (PDF available here). I've implemented this algorithm in Matlab for my own research – you can find my code on GitHub here. There are lots of optimizations for special cases and vectorization, but these highlighted lines are relatively straightforward for the real-valued case as well as the general complex case. I had started a C version a while back, but never got around to completing it.
In Matlab, evaluating this numerically is 3+ orders of magnitude faster than evaluating it symbolically. If your argument $z$ is constrained in particular ways (e.g., real-valued), you may be able to simplify your algorithm – see the Lawrence, et al. paper and the comments in my wrightOmega code.
Apparently SciPy also has an implementation, scipy.special.wrightomega, that you may be able to browse the source code for.
