# Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets

## TL;DR

This paper introduces new classes of wavelet functions derived from generalized Clifford-Jacobi polynomials, extending fractional calculus into Clifford analysis, with proven reconstruction and Fourier rules.

## Contribution

It extends fractional calculus to Clifford analysis, creating new wavelet functions based on generalized Jacobi polynomials with proven mathematical properties.

## Key findings

- New monogenic polynomial classes based on 2-parameter weight functions
- Introduction of novel wavelet functions from these polynomials
- Established reconstruction and Fourier-Plancherel formulas

## Abstract

In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight functions which extend the classical Jacobi ones in the context of Clifford analysis. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved. The main tool reposes on the extension of fractional derivatives, fractional integrals and fractional Fourier transforms to Clifford analysis.