# The convergence of discrete Fourier-Jacobi series

## TL;DR

This paper investigates the convergence behavior of discrete Fourier-Jacobi series by analyzing the associated partial sum operators within the context of $ ext{ell}^p( ext{N})$-norms, providing new insights into their convergence properties.

## Contribution

It introduces a discrete analogue of the Fourier-Jacobi series convergence problem and characterizes the convergence of partial sum operators in $ ext{ell}^p( ext{N})$-norms.

## Key findings

- Characterization of convergence of partial sum operators in $ ext{ell}^p( ext{N})$-norms.
- Extension of Fourier-Jacobi series convergence analysis to discrete settings.

## Abstract

The discrete counterpart of the problem related to the convergence of the Fourier-Jacobi series is studied. To this end, given a sequence, we construct the analogue of the partial sum operator related to Jacobi polynomials and characterize its convergence in the $\ell^p(\mathbb{N})$-norm.