Legendre-Stieltjes Polynomial

Let $n$ be a non-negative integer and $x$ a real number with $-1\leqslant x\leqslant 1$, the Legendre-Stieltjes polynomial $E_n$ is defined by the property below \[ \int_{-1}^1 E_{n+1}(x)P_n(x)x^k dx=0,\quad \text{for}\; k=0,1,\ldots,n \] where $P_n(x)$ is the Legendre polynomial. This application evaluates Legendre-Stieltjes polynomial $E_n(x)$, the derivative $E'_n(x)$, and the zeros of $E_n(x).$

Legendre-Stieltjes Polynomial Calculator