/// <summary>
/// Returns the value of the Associated Laguerre polynomial of degree <paramref name="n"/> and order <paramref name="m"/> at point <paramref name="x"/>
/// </summary>
/// <param name="n">Polynomial degree. Requires <paramref name="n"/> ≥ 0. Limited to <paramref name="n"/> ≤ 127</param>
/// <param name="m">Polynomial order. Requires <paramref name="m"/> ≥ 0</param>
/// <param name="x">Polynomial argument</param>
public static double LaguerreL(int n, int m, double x)
{
if ((n < 0) || (m < 0))
{
Policies.ReportDomainError("LaguerreL(n: {0}, m: {1}, x: {2}): Requires n,m >= 0", n, m, x);
return(double.NaN);
}
if (n >= 128)
{
Policies.ReportNotImplementedError("LaguerreL(n: {0}, m: {1}, x: {2}): Not implemented for n >= 128", n, m, x);
return(double.NaN);
}
// Special cases:
if (m == 0)
{
return(Math2.LaguerreL(n, x));
}
if (n == 0)
{
return(1);
}
if (double.IsNaN(x))
{
Policies.ReportDomainError("LaguerreL(n: {0}, m: {1}, x: {2}): NaN not allowed", n, m, x);
return(double.NaN);
}
if (double.IsInfinity(x))
{
return((x > 0 && IsOdd(n)) ? double.NegativeInfinity : double.PositiveInfinity);
}
// use recurrence
// p0 - current
// p1 - next
double p0 = 1;
double p1 = m + 1 - x;
for (uint k = 1; k < (uint)n; k++)
{
double next = ((2 * k + (uint)m + 1 - x) * p1 - (k + (uint)m) * p0) / (k + 1);
p0 = p1;
p1 = next;
}
return(p1);
}
