User:Egm6341.s11.team4.kurth/hw6

=Problem 6.5: Using the Recurrence Relation to Calculate Polynomials $$p_{2i}(t)$$ and $$p_{2i+1}(t)$$=

Objective
Use the recurrence relation, equation [[media:Nm1.s11.mtg32.djvu|(1)p.32-2]]

to find $$\displaystyle \;\; (p_2,p_3),\;(p_4,p_5),\;(p_6,p_7),\;(p_8,p_9)$$.

Solution
From equations [[media:Nm1.s11.mtg32.djvu|(1)p.32-1]] and [[media:Nm1.s11.mtg32.djvu|(3)-(4)p.32-1]] the polynomials $$\displaystyle p_{2i}(t)$$ and $$\displaystyle p_{2i+1}(t)$$ take the following form:

Find $$(p_2,p_3)$$
Here, $$\displaystyle i=1$$. Equation (5.2) becomes

Using equations (5.3) and (5.4) to reconstruct $$\displaystyle p_2$$ and $$\displaystyle p_3$$

Find $$(p_4,p_5)$$
Now, $$\displaystyle i=2$$. Equation (5.2) becomes

Using equations (5.3) and (5.4) to reconstruct $$\displaystyle p_4$$ and $$\displaystyle p_5$$

Find $$(p_6,p_7)$$
Now, $$\displaystyle i=3$$. Equation (5.2) becomes

Using equations (5.3) and (5.4) to reconstruct $$\displaystyle p_6$$ and $$\displaystyle p_7$$

Find $$(p_8,p_9)$$
Now, $$\displaystyle i=4$$. Equation (5.2) becomes

Using equations (5.3) and (5.4) to reconstruct $$\displaystyle p_8$$ and $$\displaystyle p_9$$