- #1
rwooduk
- 762
- 59
(1) [tex]P_{l}(u)[/tex] is normalised such that [tex]P_{l}(1) = 1[/tex]. Find [tex]P_{0}(u)[/tex] and [tex]P_{2}(u)[/tex]
We have the recursion relation:
[tex]a_{n+2} = \frac{n(n+1) - l(l+1)}{(n+2)(n+1)}a_{n}[/tex]
I'm going to include a second similar question, which I'm hoping is solved in a similar way, so I can relate it to the above question:
(2) Show that the functions [tex]H_{0}(x) = 1[/tex], [tex]H_{1}(x) = 2x[/tex], [tex]H_{2}(x) = 4x^{2} - 2[/tex], [tex]H_{3}(x) = 8x^{3} - 12x[/tex] have coeffiecients that obey the recursion relation
We have the recursion relation:
[tex]a_{n+2} = \frac{2(p-n)}{(n+2)(n+1)}a_{n}[/tex]
I have the answer for (2) and it makes no sense to me, i tried to tabulate why:
For P = 0, 1, 2 we have Even [tex]a_{0}[/tex] values of 1, 0, -2 respectively
For P = 0, 1, 2 we have Odd [tex]a_{1}[/tex] values of 0, 2, 0 respectively
And for P = 0, 1, 2 we have n values of 0, 1, 0 respectively
Where do these come from? I've looked for how to solve the above problems, and can't find a step by step example anywhere, it follows no logical pattern.
Any help would be VERY much appreciated.
Thanks.
We have the recursion relation:
[tex]a_{n+2} = \frac{n(n+1) - l(l+1)}{(n+2)(n+1)}a_{n}[/tex]
I'm going to include a second similar question, which I'm hoping is solved in a similar way, so I can relate it to the above question:
(2) Show that the functions [tex]H_{0}(x) = 1[/tex], [tex]H_{1}(x) = 2x[/tex], [tex]H_{2}(x) = 4x^{2} - 2[/tex], [tex]H_{3}(x) = 8x^{3} - 12x[/tex] have coeffiecients that obey the recursion relation
We have the recursion relation:
[tex]a_{n+2} = \frac{2(p-n)}{(n+2)(n+1)}a_{n}[/tex]
I have the answer for (2) and it makes no sense to me, i tried to tabulate why:
For P = 0, 1, 2 we have Even [tex]a_{0}[/tex] values of 1, 0, -2 respectively
For P = 0, 1, 2 we have Odd [tex]a_{1}[/tex] values of 0, 2, 0 respectively
And for P = 0, 1, 2 we have n values of 0, 1, 0 respectively
Where do these come from? I've looked for how to solve the above problems, and can't find a step by step example anywhere, it follows no logical pattern.
Any help would be VERY much appreciated.
Thanks.