Legendre Series for Piecewise Analytic Functions

This repository is related to my article Exploring the Pointwise Convergence of Legendre Series for Piecewise Analytic Functions.

Contents

• legendre_series.py contains the code for computing the Legendre series and analysing the pointwise convergence.
• plots.py contains the code for plotting the results from the computations.
• scripts directory contains script files for creating the different plots.

Instructions

Install Miniconda (or Anaconda).

Install Conda environment

conda env create -f environment.yml 

Activate the environment

source activate legendre36

Create the figures

python scripts/run_legendre_polynomials.py
python scripts/run_piecewise_functions.py
python scripts/run_legendre_series.py
python scripts/run_pointwise_convergence.py
python scripts/run_convergence_distance.py

Additionally, creating the animations requires FFmpeg.

python scripts/run_animation.py