Julia package for some special functions

Jan 26, 2023

I implemented a few special functions in Julia that I had to use for my master's thesis

FewSpecialFunctions.jl

Overview

This post outlines the recent implementation of several special functions in the Julia programming language. These functions are primarily of interest in scientific and mathematical computing.

Details of the Implementations

  • The Clausen function, relevant in certain areas of number theory.

  • Coulomb wave functions, useful in quantum scattering theory.

  • Debye function, used in solid-state physics, particularly in the study of heat capacities at low temperatures.

  • Fresnel Functions, related to optics, specifically in the context of diffraction and interference.

  • Struve Function, finds use in certain wave equation solutions.

  • Hypergeometric Functions, these functions are versatile and find applications in various fields, including physics and statistics.

  • Confluent Hypergeometric Functions, a subset of hypergeometric functions, these are particularly relevant in theoretical physics.

  • Fermi-Dirac Functions, important in studying quantum systems at finite temperatures.

Poster
A few examples

Code

Code can be found here, contributions are welcome.