2x2 hypergeometric operators with diagonal eigenvalues

C. CALDERON; Y. GONZALEZ; I. PACHARONI; S. SIMONDI; I. ZURRIAN

JOURNAL OF APPROXIMATION THEORY

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2019 vol. 248

0021-9045

In this work we give all the order-two hypergeometric operators , symmetric with respect to some 2 × 2 irreducible matrix-weight on such that with no repetition among the eigenvalues , where is the (unique) sequence of monic orthogonal polynomials with respect to .We obtain a new family of such operators and weights, depending on three parameters, generalizing some older examples. We also give, in a very explicit way, the corresponding monic orthogonal polynomials, their three term recurrence relation and their squared matrix-norms.