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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.
q = [1 0]\((2n+1-x) L_n(x) - n L_{n-1}(x)\)\((2n+1)L_n(x) - xL_n(x) - n L_{n-1}(x)\)

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.