pollegendre

Function: pollegendre
Section: polynomials
C-Name: pollegendre_eval0
Prototype: LDGD0,L,
Help: pollegendre(n,{a='x},{flag=0}): legendre polynomial of degree n evaluated
 at a. If flag is 1, return [P_{n-1}(a), P_n(a)].
Description:
  (small,?var):gen    pollegendre($1,$2)
  (small,gen):gen     pollegendre_eval($1,$2)
Doc: $n^{\text{th}}$ \idx{Legendre polynomial} $P_n$ evaluated at $a$ (\kbd{'x}
 by default), where
 $$P_n(x) = \dfrac{1}{2^n n!} \dfrac{d^n}{dx^n}(x^2-1)^n\;.$$
 If \fl\ is 1, return $[P_{n-1}(a), P_n(a)]$.
Variant: To obtain the $n$-th Legendre polynomial $P_n$ in variable $v$,
 use \fun{GEN}{pollegendre}{long n, long v}. To obtain $P_n(a)$,
 use \fun{GEN}{pollegendre_eval}{long n, GEN a}.