Division Problem of a Regular Form: The Case x2u=λxv

Abstract

We present a systematic study of a regular linear functional v to find all regular forms u which satisfy the equation x2u=λxv, λ∈ℂ−{0}. We also give the second-order recurrence relation of the orthogonal polynomial sequence with respect to u and study the semiclassical character of the found families. We conclude by treating some examples.