Exercises 15.5 Homework
1.
Adapt Example 15.4.1 to Laguerre polynomials. That is, compute and plot Laguerre polynomials up to degree 10. Use \([0, 5]\) as an interval for plotting since we cannot plot on \([0, \infty)\text{.}\) Also, comment on some pattern you observe in their behavior.
Hint
Note that the degree 1 polynomial is no longer
q = [1 0]. Also, the recursive formula needs to be changed. When changing it, think of \((2n+1-x) L_n(x) - n L_{n-1}(x)\) as \((2n+1)L_n(x) - xL_n(x) - n L_{n-1}(x)\) and find the vector of coefficients for each of these three terms.2.
Adapt Example 15.4.2 to Laguerre polynomials. That is, compute and plot the roots of Laguerre polynomials of degrees 2 to 10. Also, comment on some pattern you observe in their behavior.