A Class of Non-Symmetric Semi-Classical Linear Forms

We show that if v is a regular semi-classical form (linear functional), then the form u defined by (x ？ τ 2 )σu = ？λv and σ(x ？ τ )u = 0 where σu is the even part of u, is also regular and semi-classical form for every complex λ except for a discrete set of numbers depending on v. We give explicitly the recurrence coefficients and the structure relation coefficients of the orthogonal polynomials sequence associated with u and the class of the form u knowing that of v. We conclude with illustrative examples.