Legendre

Methods

📄️ GetLegendreRecurrenceCoeff

Recurrence coefficients are for monic and nonmonic Legendre polynomials.

📄️ LegendreAlpha

Recurrence coeff for Legendre polynomial.

📄️ LegendreBeta

Recurrence coeff for Legendre polynomial.

📄️ LegendreDMatrix

Interface

📄️ LegendreEval

Evaluate Legendre polynomials of order n at single or several points.

📄️ LegendreEvalAll

Evaluate Legendre polynomials from order = 0 to n at single or several points.

📄️ LegendreEvalSum

Evaluate the finite sum of Legendre polynomials at point x.

📄️ LegendreGaussLobattoQuadrature

This routine returns the $n+2$ Quadrature points and weights.

📄️ LegendreGaussQuadrature

This routine computes the n Gauss-Quadrature points.

📄️ LegendreGaussRadauQuadrature

This routine returns the $n+1$ Quadrature points and weights.

📄️ LegendreGradientCoeff

This routine returns the coefficients of gradient of Legendre expansion.

📄️ LegendreGradientEval

Evaluate gradient of Legendre polynomials.

📄️ LegendreGradientEvalAll

Evaluate gradient of Legendre polynomials.

📄️ LegendreGradientEvalSum

Evaluate finite sum of gradient of Legendre polynomials.

📄️ LegendreInvTransform

Discrete Inverse Legendre transform.

📄️ LegendreJacobiLobattoMatrix

Legendre Lobatto matrix for Jacobi polynomial.

📄️ LegendreJacobiMatrix

Legendre matrix for Jacobi polynomials.

📄️ LegendreJacobiRadauMatrix

Radau matrix for Legendre polynomials.

📄️ LegendreLeadingCoeff

Leading coefficient of Legendre polynomials.

📄️ LegendreLeadingCoeffRatio

Ratio of Leading coefficient of Legendre polynomials.

📄️ LegendreNormSQR

Square norm of Legendre polynomial.

📄️ LegendreNormSQR2