Characterization of the D w -Laguerre – Hahn Functionals M. FOUPOUAGNIGNI a, * and F. MARCELLA ´ N b a De ´ partement de Mathe ´ matiques, Ecole Normale Supe ´ rieure, Universite ´ de Yaounde ´ I, BP 47 Yaounde ´, Cameroon; b Departamento de Matema ´ ticas, Escuela Polite ´cnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Legane ´ s, Madrid, Spain (Received 26 February 2001; Revised 7 August 2001; In final form 14 November 2001) We give some characterization theorems for the D w Laguerre Hahn linear functionals and we extend the concept of the class of the usual Laguerre Hahn functionals to the D w Laguerre Hahn functionals, recovering the classic results when w tends to zero. Moreover, we show that some transformations carried out on the D w Laguerre Hahn linear functionals lead to new D w Laguerre Hahn linear functionals. Finally, we analyze the class of the resulting functionals and we give some applications relative to the first associated Charlier, Meixner, Krawtchouk and Hahn orthogonal polynomials. Keywords: Regular linear functionals; Orthogonal polynomials; Stieltjes functions; Riccati difference equation; Laguerre Hahn class; D w Laguerre Hahn class ISSN 1023-6198 print/ISSN 1563-5120 online q 2002 Taylor & Francis Ltd DOI: 10.1080/1023619021000000726 *Corresponding author. E mail: foupoua@uycdc.uninet.cm Journal of Difference Equations and Applications, 2002 Vol. 8 (8), pp. 689 717 1