using python

[a] (6 points) - Another very important class of special functions are called the Laguerre Polynomials, say Ln(x), which are defined for non-negative integer n via the series K-0 Using a for -loop, vectorized, recursive approach, write a function which computes the Laguerre functions for any non-negative integer n [b] (3 points). Make a plot showing Ln(x) for n = 0, l , 2, 3, 4 on the same graph, using different colors for each different n. c] (2 points) The plot should have a legend as well as appropriately labeled axes. [d] (3 points) Write down the expression for Lo(x) and L1(x) by replacing n with 0 and 1 respectively in the equation for L,(x) above. Compare your expression for Lo(x) and Li(x) with the graph in Problem 4b. Discuss your observations