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