legendre_p_tilde.m

   1 function P_tilde = legendre_p_tilde(n, a, b)
   2   % Return the `n`th Legendre polynomial scaled to the interval [a,b].
   3   %
   4   % INPUT:
   5   %
   6   %   * ``n`` - The index of the polynomial that we want.
   7   %
   8   %   * ``a`` - The left endpoint of the interval.
   9   %
  10   %   * ``b`` - The right endpoint of the interval.
  11   %
  12   % OUTPUT:
  13   %
  14   %   * ``P_tilde`` - A polynomial function of one argument.
  15   %
  16   if (n < 0)
  17     % Can't do anything here. Return nothing.
  18     P = NA;
  19   else
  20     % Compute the Legendre polynomial over [-1,1] and mangle it to fit
  21     % the interval [a,b].
  22     P = legendre_p(n);
  23     P_tilde = @(x) P( (2/(b-a)).*x + 1 - (2*b)/(b-a) );
  24   end
  25 end