Open wavefunction91 opened 1 year ago
The Gauss-Jacobi quadrature integrates functions of the form
$$ \int{-1}^1 f(x) (1-x)^\alpha (1+x)^\beta\mathrm{d}x \approx \sum{i=1}^n w_i f(x_i) $$
where ${x_i}$ are the nodes of $n$-th order Jacobi polynomial, $P^{(\alpha,\beta)}_n$. The Chebyshev and Legendre polynomials are special cases of the polynomials which already have quadrature rules generated.
The Gauss-Jacobi quadrature integrates functions of the form
$$ \int{-1}^1 f(x) (1-x)^\alpha (1+x)^\beta\mathrm{d}x \approx \sum{i=1}^n w_i f(x_i) $$
where ${x_i}$ are the nodes of $n$-th order Jacobi polynomial, $P^{(\alpha,\beta)}_n$. The Chebyshev and Legendre polynomials are special cases of the polynomials which already have quadrature rules generated.