OrthogonalPolynomialsLegendreP(Int32, Int32, Double) Method

Computes the value of an associated Legendre polynomial.

Definition

Namespace: Meta.Numerics.Functions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 4.2.0+6d77d64445f7d5d91b12e331399c4362ecb25333

C#

public static double LegendreP(
	int ell,
	int m,
	double x
)

VB

Public Shared Function LegendreP ( 
	ell As Integer,
	m As Integer,
	x As Double
) As Double

C++

public:
static double LegendreP(
	int ell, 
	int m, 
	double x
)

F#

static member LegendreP : 
        ell : int * 
        m : int * 
        x : float -> float

ell Int32: The order, which must be non-negative.
m Int32: The associated order, which must lie between -ℓ and +ℓ inclusive.
x Double: The argument, which must lie on the closed interval between -1 and +1.

Double
The value of P_l,m(x).

Associated Legendre polynomials appear in the definition of the SphericalHarmonic(Int32, Int32, Double, Double) functions.

For values of l and m over about 150, values of this polynomial can exceed the capacity of double-wide floating point numbers.

ell is negative, m lies outside {-ℓ .. +ℓ}, or x lies outside [-1, +1].