model::GaussLegendreRecursiveRelation Struct Reference

The P_n(x) = (2n-1)/n * x * P_(n-1) - (n-1)/n * P_(n-2). More...

#include <GaussLegendreRecursiveRelation.h>

Collaboration diagram for model::GaussLegendreRecursiveRelation:

Static Public Member Functions
static double	a (const int &n)
	Class template defining the coefficients A, B and C of the recursive relation for orthogonal Legendre polinomials: P_n(x) = (A_n*x+B_n) * P_(n-1) - C_n * P_(n-2).
static double	b (const int &n)
	The coefficient b.
static double	c (const int &n)
	The coefficient c.

Detailed Description

The P_n(x) = (2n-1)/n * x * P_(n-1) - (n-1)/n * P_(n-2).

gives: A_n = (2*n-1)/n B_n = 0 C_n = (n-1)/n

References: [1] Golub, G.H., and Welsch, J.H. 1969, "Calculation of Gauss Quadrature Rules", Mathematics of Computation, vol. 23, pp. 221–230.

[2] Press, W. et al. "Numerical Recipes", 3rd edition, p.188.

Definition at line 37 of file GaussLegendreRecursiveRelation.h.

Member Function Documentation

a()

auto model::GaussLegendreRecursiveRelation::a ( const int & n )

static

Class template defining the coefficients A, B and C of the recursive relation for orthogonal Legendre polinomials: P_n(x) = (A_n*x+B_n) * P_(n-1) - C_n * P_(n-2).

The coefficient a

Definition at line 7 of file GaussLegendreRecursiveRelation.cpp.

b()

auto model::GaussLegendreRecursiveRelation::b ( const int & n )

static

The coefficient b.

Definition at line 12 of file GaussLegendreRecursiveRelation.cpp.

c()

auto model::GaussLegendreRecursiveRelation::c ( const int & n )

static

The coefficient c.

Definition at line 17 of file GaussLegendreRecursiveRelation.cpp.

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The documentation for this struct was generated from the following files:

• GaussLegendreRecursiveRelation.h
• GaussLegendreRecursiveRelation.cpp