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Differential operators having Sobolev type Laguerre polynomials as eigenfunctions

Authors:	H. Bavinck

Affiliation:	Delft University of Technology, Faculty of Technical Mathematics and Informatics, Mekelweg 4, 2628 CD Delft, The Netherlands

Abstract:	We consider the polynomials $left{ L_n^{alpha ,M}(x,l)right} _{n=0}^infty$ orthogonal with respect to the Sobolev type inner product $begin{equation}leftlangle p,qrightrangle =frac 1{Gamma (alpha +1)}int _0^infty p(x)q(x)x^alpha e^{-x}dx+Mp^{(l)}(0)q^{(l)}(0), end{equation}$ where and is a nonnegative integer. It is the purpose of this paper to show that these polynomials are eigenfunctions of a class of linear differential operators containing one that is of finite order if is a nonnegative integer and

Keywords:	Differential operators Sobolev type Laguerre polynomials

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