DIFFERENTIAL-OPERATORS HAVING SOBOLEV TYPE LAGUERRE-POLYNOMIALS AS EIGENFUNCTIONS

We consider the polynomials {L-n(alpha,m)(x,1)}(n=0)(infinity) orthogo nal with respect to the Sobolev type inner product [p,q] = 1/Gamma(alp ha + 1) integral(0)(infinity) p(x)q(x)x(alpha)e(-x)dx + Mp((l))(0)q((i ))(0), where alpha > -1, M greater than or equal to 0 and l is a nonne gative integer. It is the purpose of this paper to show that these pol ynomials are eigenfunctions of a class of linear differential operator s containing one that is of finite order 2 alpha + 4l + 4 if alpha is a nonnegative integer and M > 0.