| Lie Group | Special Function |
| Heisenberg group H3 | Hermite polynomials |
| Euclidean group E2 | Bessel functions |
| Special unitary group | Legendre polynomials |
|
| Jacobi Polynomials |
| Special linear group | Hypergeometric functions |
| Third order triangular matrices | Whittaker functions |
|
| Laguerre polynomials |
| Special orthogonal group | Gegenbauer functions |