Orthogonal polynomials on the real and the imaginary axes in the complex plane

S. M. Zagorodnyuk

Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002) no. 3, pp. 502-508

Résumé

In this paper systems of polynomials satisfying a five-term reccurent relation, which can be written in a matrix form $J_5 p(\lambda)= \lambda^2 p(\lambda)$, where $p(\lambda)=(p_0(\lambda),p_1(\lambda),\dots,p_n(\lambda), \dots)^T$ is a vector of polynomials, $J_5$ is a semi-infinite, five-diagonal, Hermitian matrix are considered. The such kind systems which also satisfy the relation $J_3 p=\lambda p$, where $J_3$ is a Jacobi matrix, are considered. A parameteric form of some such systems and matrices is obtained. Formulas of orthonormality for some of the systems are also obtained.