legendre_p.m

   1 function P = legendre_p(n)
   2   ## Return the `n`th Legendre polynomial.
   3   ##
   4   ## INPUT:
   5   ##
   6   ##   * ``n`` - The index of the polynomial that we want.
   7   ##
   8   ## OUTPUT:
   9   ##
  10   ##   * ``P`` - A polynomial function of one argument.
  11   ##
  12   if (n < 0)
  13     ## Can't do anything here. Return nothing.
  14     P = NA;
  15   elseif (n == 0)
  16     ## One of our base cases.
  17     P = @(x) 1;
  18   elseif (n == 1)
  19     ## The second base case.
  20     P = @(x) x;
  21   else
  22     ## Not one of the base cases, so use the recursive formula.
  23     prev = legendre_p(n-1);
  24     prev_prev = legendre_p(n-2);
  25     P = @(x) (1/n).*( (2*n - 1).*x.*prev(x) - (n-1).*prev_prev(x) );
  26   end
  27 end