template<size_t K>
Rodin::Variational::JacobiPolynomial class

Jacobi polynomial evaluator.

Template parameters
K Polynomial degree.

Evaluates the Jacobi polynomial $ P_K^{(\alpha, \beta)}(x) $ and its derivative $ \partial_x P_K^{(\alpha, \beta)}(x) $ using:

  • the three-term recurrence for $ P_n^{(\alpha,\beta)} $

  • the identity

    \[ \frac{d}{dx} P_K^{(\alpha, \beta)}(x) = \frac{1}{2}\bigl(K + \alpha + \beta + 1\bigr) P_{K - 1}^{(\alpha + 1, \beta + 1)}(x). \]

Public static functions

static void getValue(Real& P, Real& dP, Real alpha, Real beta, Real x) constexpr
Computes $ P_K^{(\alpha, \beta)}(x) $ and $ \partial_x P_K^{(\alpha, \beta)}(x) $ .

Function documentation

template<size_t K>
static void Rodin::Variational::JacobiPolynomial<K>::getValue(Real& P, Real& dP, Real alpha, Real beta, Real x) constexpr

Computes $ P_K^{(\alpha, \beta)}(x) $ and $ \partial_x P_K^{(\alpha, \beta)}(x) $ .

Parameters
P out Value of $ P_K^{(\alpha, \beta)}(x) $ .
dP out Value of $ \partial_x P_K^{(\alpha, \beta)}(x) $ .
alpha in First Jacobi parameter $ \alpha $ .
beta in Second Jacobi parameter $ \beta $ .
x in Evaluation point.