alp {cooltools} | R Documentation |

## Associated Legendre Polynomials

### Description

Compute associated Legendre polynomials P_l^m(x), defined as the canonical solutions of the general Legendre equation. These polynomials are used, for instance, to compute the spherical harmonics.

### Usage

```
alp(x, l = 0, m = 0)
```

### Arguments

`x` |
real argument between -1 and +1, can be a vector |

`l` |
degree of the polynomial (0,1,2,...); accurate to about 25 |

`m` |
order of the polynomial (-l,-l+1,...,l); for negative values the standard convention is used: if m>0, then P(x,l,-m) = P(x,l,m) (-1)^m*factorial(l-m)/factorial(l+m). |

### Value

Returns a vector with the same number of elements as `x`

### Author(s)

Danail Obreschkow

### See Also

[Package

*cooltools*version 2.4 Index]