# Special Functions

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Clebsch-o-matic Has 3j, 6j, and 9j symbols!

### Clebsch-Gordon Coefficients

Notation: (Condon-Shortly convention).

For fractional spins use, eg., "1/2".

### Wigner (simplified) Rotation Matrices

Notation: d^{(j)}_{m n } (Rose convention).

### Legendre Polynomials

Notation: P_{l}(x).

### Associated Legendre Polynomials

Notation: P^{m}_{l}(x).

### Hermite Polynomials

Notation: H_{n}(x).

### Spherical Harmonics

Notation: Y_{lm} (fixed May 2002)

### Associated Laguerre Polynomials

Notation: L^{m}_{l}(x).

NB: to get the Laguerre polynomial L_{l}(x), set m=0.

### regular spherical Bessel Function

Notation: j_{l}(x).

### irregular spherical Bessel Function

Notation: n_{l}(x).