  We study the orthogonal complement of the Hilbert subspace considered by by
van Eijndhoven and Meyers in [J. Math. Anal. Appl. 146 (1990), no. 1, 89--98}
and associated to holomorphic Hermite polynomials. A polyanalytic orthonormal
basis is given and the explicit expressions of the corresponding reproducing
kernel functions and Segal--Bargmann integral transforms are provided.
