On Sobolev Orthogonality for the Generalized Laguerre Polynomials

✍ Scribed by Teresa E. Pérez; Miguel A. Piñar

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 359 KB
• Volume: 86
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0069

✦ Synopsis

The orthogonality of the generalized Laguerre polynomials, [L (:) n (x)] n 0 , is a well known fact when the parameter : is a real number but not a negative integer. In fact, for &1<:, they are orthogonal on the interval [0, + ) with respect to the weight function (x)=x : e &x , and for :<&1, but not an integer, they are orthogonal with respect to a non-positive definite linear functional. In this work we will show that, for every value of the real parameter :, the generalized Laguerre polynomials are orthogonal with respect to a non-diagonal Sobolev inner product, that is, an inner product involving derivatives.