On meromorphic harmonic functions with a pole at the origin

In this article, we investigate meromorphic univalent harmonic functions having a simple pole at the origin. First we establish sufficient conditions for the univalence of function f within the broader class of meromorphic harmonic functions. Then, we derive coefficient estimate for some geometric subclasses of meromorphic univalent harmonic functions. Subsequently, we provide several necessary and sufficient conditions for f to be hereditarily \(\lambda \) $\lambda$ -spirallike. Finally, we offer a comprehensive characterization of hereditarily meromorphic harmonic Archimedean and hyperbolic spirallike functions.