2
votes
0answers
87 views

Perturbation analysis for three term recurrences

Jacobi polynomials, denoted by $J^{(\alpha,\beta)}_n$, on $[-1,1]$ satisfy a three term recurrence $$ J_{n+1}^{(\alpha,\beta)}(x) = (A_n+B_nx)J^{(\alpha,\beta)}_n + C_nJ_{n-1}^{(\alpha,\beta)}(x), ...
2
votes
1answer
565 views

Three term recurrence relation.

For given $n,\ell\in\mathbb N_0$, I am interested in studying the following recursion relation for some $\mu\in\mathbb R$: $$\sqrt{-1} \tfrac{j(\ell-j+1)(n-j+1)(n+j+1)}{2(2j-1)(2j+1)} a_{j-1} - ...