# New type of monogenic polynomials and associated spheroidal wavelets

## TL;DR

This paper introduces new monogenic polynomials in Clifford analysis based on two-parameter weight functions, extending classical Jacobi-Gegenbauer polynomials, and develops associated spheroidal wavelets with proven reconstruction and Fourier rules.

## Contribution

It presents novel monogenic polynomial classes and constructs new spheroidal wavelets, expanding the mathematical tools in Clifford analysis.

## Key findings

- New monogenic polynomial classes based on 2-parameter weights
- Extension of Jacobi-Gegenbauer polynomials
- Development of associated spheroidal wavelets with proven properties

## Abstract

In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well known Jacobi-Gegenbauer ones. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved.