Heun functions are direct generalizations of hypergeometric functions and occur in quantum mechanics, mathematical physics and other applications. The Wolfram Language provides full coverage of the Heun functions and their derivatives, with arbitrary-precision numerical evaluation for complex values of all parameters, as well as symbolic transformations and simplifications.

General Heun Functions

HeunG  ▪  HeunGPrime

Confluent Heun Functions

HeunC  ▪  HeunCPrime

Double-Confluent Heun Functions

HeunD  ▪  HeunDPrime

Bi-Confluent Heun Functions

HeunB  ▪  HeunBPrime

Tri-Confluent Heun Functions

HeunT  ▪  HeunTPrime

Lamé Functions

LameC  ▪  LameS  ▪  LameCPrime  ▪  LameSPrime  ▪  LameEigenvalueA  ▪  LameEigenvalueB