# On slice polyanalytic functions of a quaternionic variable

## TL;DR

This paper introduces quaternionic slice polyanalytic functions, explores their properties, and applies these findings to study quaternionic Fock and Bergman spaces, including explicit reproducing kernels.

## Contribution

It defines and analyzes quaternionic slice polyanalytic functions and extends the theory to quaternionic Fock and Bergman spaces with explicit kernel formulas.

## Key findings

- Defined quaternionic slice polyanalytic functions
- Derived properties of these functions
- Explicitly computed reproducing kernels for associated spaces

## Abstract

In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In particular, we give explicit expressions of their reproducing kernels.