MP4 · Special functions
A 26-module path through mp4 · special functions, in study order from foundations to the frontier.
Modules
- Gamma Function
- Beta Function
- Analytic Continuation and Poles of the Gamma Function
- Orthogonal Polynomials: General Theory
- Generating Functions for Special Functions
- Recurrence Relations for Special Functions
- Bessel Functions of the First and Second Kind
- Modified Bessel Functions
- Spherical Bessel Functions
- Hankel Functions and Asymptotic Behavior of Bessel Functions
- Legendre Polynomials
- Associated Legendre Functions
- Spherical Harmonics
- Hermite Polynomials
- Laguerre and Associated Laguerre Polynomials
- Gegenbauer and Chebyshev Polynomials
- Jacobi Polynomials
- Gaussian Hypergeometric Function
- Confluent Hypergeometric Functions
- Generalized Hypergeometric Functions
- Sturm-Liouville Theory and Special Functions
- Addition Theorems for Special Functions
- Asymptotic Expansions of Special Functions
- Watson-Sommerfeld and Integral Representations
- Special Function Identities from Group Representation Theory
- q-Special Functions and Basic Hypergeometric Series