Journal of Computational and Applied Mathematics 49 (1993) 51-57 North-Holland 51 CAM 1415 Real orthogonalizing weights for Bessel polynomials W.D. Evans zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA School of Mathematics, University of W ales, CardifJ United Kingdom W.N. Everitt * Department of Mathematics, The University of Birmingham, United Kingdom K.H. Kwon *,** Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon, South Korea L.L. Littlejohn * Department of Mathematics, Utah State University, Logan, UT, United States Received 12 February 1992 Revised 2 April 1992 Abstract Evans, W.D., W.N. Everitt, K.H. Kwon and L.L. Littlejohn, Real orthogonalizing weights for Bessel polynomials, Journal of Computational and Applied Mathematics 49 (1993) 51-57. We construct real orthogonalizing weights of bounded variation for the generalized Bessel polynomials. Keywords: Generalized Bessel polynomials; real orthogonalizing weights zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR 1. Introduction It is well known that there are essentially four distinct orthogonal polynomial sets (OPSs in short), i.e., three classical OPSs (Jacobi, Laguerre, Hermite polynomials) and Bessel polynomi- als, which arise as polynomial solutions of a(x)y;(x)+7(X)y~(X)-AA,y,(X)=0, n=0,1,2,..., (1.1) Correspondence to: Prof. L.L. Littlejohn, Department of Mathematics & Statistics, Utah State University, Logan, UT 84322-3900, United States. e-mail: lance@sunfs.math.usu.edu. * These authors express their thanks to the first author for his hospitality during their visit to the University of Wales. * * This author is partially supported by KOSEF and GARC. 0377-0427/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved SSDZ 0377-0427(93)E0042-K