alp {cooltools}

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

sphericalharmonics