function P_tilde = legendre_p_tilde(n, a, b) % Return the `n`th Legendre polynomial scaled to the interval [a,b]. % % INPUT: % % * ``n`` - The index of the polynomial that we want. % % * ``a`` - The left endpoint of the interval. % % * ``b`` - The right endpoint of the interval. % % OUTPUT: % % * ``P_tilde`` - A polynomial function of one argument. % if (n < 0) % Can't do anything here. Return nothing. P = NA; else % Compute the Legendre polynomial over [-1,1] and mangle it to fit % the interval [a,b]. P = legendre_p(n); P_tilde = @(x) P( (2/(b-a)).*x + 1 - (2*b)/(b-a) ); end end