Laurent series with respect to a matrix ball from the space $\mathbb C^n \left[ m\times m \right]$

In this work we suggest analogues of the Laurent series with respect to a matrix ball from the space $\mathbb C^n\left[ m\times m \right]$. For this purpose we introduce first the notion of the layer of a matrix ball in $\mathbb C^n\left[ m\times m \right]$, and then we use the properties of the Bochner-Luogeng type intergrals in this layer to obtain the analogues of the Laurent series.