(30 pts.) The gamma function is defined by 0 It is known that for integer numbers the function has the value (We define O!1.) Thus, for example, (1,1),(2,1),(3,2),(4,6),(5,24) can be used as data points for an interpolating polynomial (a) Write a MATLAB script that computes the polynomial interpolant of degree four that passes through the above five data points. b) Write a program that computes a cubic spline to interpolate the same data. (You may use (c) Plot the two interpolants you found on the same graph, along with a plot of the gamma function (d) Plot the errors in the two interpolants on the same graph. What are your observations? MATLAB's spline.) itself, which can be produced using the MATLAB command gamma. (30 pts.) The gamma function is defined by 0 It is known that for integer numbers the function has the value (We define O!1.) Thus, for example, (1,1),(2,1),(3,2),(4,6),(5,24) can be used as data points for an interpolating polynomial (a) Write a MATLAB script that computes the polynomial interpolant of degree four that passes through the above five data points. b) Write a program that computes a cubic spline to interpolate the same data. (You may use (c) Plot the two interpolants you found on the same graph, along with a plot of the gamma function (d) Plot the errors in the two interpolants on the same graph. What are your observations? MATLAB's spline.) itself, which can be produced using the MATLAB command gamma