  Using the machinery of unitary spherical harmonics due to Koornwinder,
Folland and other authors, we~obtain expansions for the Szeg\"o and the
weighted Bergman kernels of $M$-harmonic functions, i.e.~functions annihilated
by the invariant Laplacian on the unit ball of the complex $n$-space. This
yields, among others, an explicit formula for the $M$-harmonic Szeg\"o kernel
in terms of multivariable as well as single-variable hypergeometric functions,
and also shows that most likely there is no explicit (``closed'') formula for
the corresponding weighted Bergman kernels.
