Laurent-Hua Loo-Keng series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$

The aim of this work is to obtain multidimensional analogs of the Laurent series with respect to the matrix ball from space ${{\mathbb{C}}^{n}}\left[ m\times m \right]$. To do this, we first introduce the concept of a "layer of the matrix ball" from ${{\mathbb{C}}^{n}}\left[ m\times m \right]$, then in this layer of the matrix ball we use the properties of integrals of the Bochner-Hua Loo-Keng type to obtain analogs of the Laurent series.