Class GaussLaguerreWeightAndAbscissaFunction

  • All Implemented Interfaces:

    public class GaussLaguerreWeightAndAbscissaFunction
    extends Object
    implements QuadratureWeightAndAbscissaFunction
    Class that generates weights and abscissas for Gauss-Laguerre quadrature. The weights $w_i$ are given by: $$ \begin{align*} w_i = -\frac{\Gamma(\alpha + n)}{n!L_i'(x_i)L_{i-1}(x_i)} \end{align*} $$ where $x_i$ is the $i^{th}$ root of the orthogonal polynomial, $L_i$ is the $i^{th}$ polynomial and $L_i'$ is the first derivative of the $i^{th}$ polynomial. The orthogonal polynomial is generated by LaguerrePolynomialFunction.
    • Constructor Detail

      • GaussLaguerreWeightAndAbscissaFunction

        public GaussLaguerreWeightAndAbscissaFunction()
        Creates an instance. Sets $\alpha = 0$
      • GaussLaguerreWeightAndAbscissaFunction

        public GaussLaguerreWeightAndAbscissaFunction​(double alpha)
        Creates an instance.
        alpha - The value of $\alpha$ to use when generating the polynomials.