A Characterization of L-orthogonal Polynomials from Three Term Recurrence Relations

Abstract

We consider the sequence of polynomials {Q (n) } satisfying the L-orthogonality a"(3)[z (-n+m) Q (n) (z)]=0, 0a parts per thousand currency signma parts per thousand currency signn-1, with respect to a linear functional a"(3) for which the moments a"(3)[t (n) ]=mu (n) are all complex. Under certain restriction on the moment functional these polynomials also satisfy a three term recurrence relation. We consider three special classes of such moment functionals and characterize them in terms of the coefficients of the associated three term recurrence relations. Relations between the polynomials {Q (n) } associated with two of these special classes of moment functionals are also given. Examples are provided to justify this characterization.