8 docs tagged with "orthogonal"

Methods

Jacobi polynomial of order $n$ is denoted by $P_^{\alpha,\beta}\left(x\right)$. Here $\alpha$ and $\beta$ are parameters of Jacobi polynomial. Note that

Methods

Methods

Methods

Methods

Jacobi polynomial with $\alpha=\beta>-1$, are called the ultraspherical polynomials or Gegenbauer polynomial. We will denote ultraspherical polynomial by $P_^{\lambda}(x)$ where, $\alpha=\lambda-\frac{1}{2}$. Note that $\lambda>-\frac{1}{2}$.