Classical orthogonal polynomials with respect to a lowering operator generalizing the Laguerre operator

References

• Al-Salam , W. 1990 . “ Characterization theorems for orthogonal polynomials ” . In Orthogonal Polynomials: Theory and Practice , Edited by: Nevai , P. Vol. 294 , 1 – 24 . Dordrecht : Kluwer Academic Publishers . NATO ASI Series C
   Google Scholar
• Angelescu , A. 1921–1923 . Sur les polynômes orthogonaux en rapport avec d'autres polynômes . Bull. Soc. Sc. Cluj Romania , 1 : 44 – 59 .
   Google Scholar
• Appell , P. 1880 . Sur une classe de polynômes . Ann. Sci. Ecole Norm. Sup. , 9 ( 2 ) : 119 – 144 .
   Google Scholar
• Ben Cheikh , Y. 2002 . On obtaining dual sequences via quasi-monomiality . Georgian Math. J. , 9 : 413 – 422 .
   Google Scholar
• Branquinho , A. , Petronilho , J. and Marcellán , F. 1994 . Classical orthogonal polynomials, a functional approach . Acta Appl. Math. , 34 : 283 – 303 . (doi:10.1007/BF00998681)
   Web of Science ®Google Scholar
• Chihara , T. S. 1978 . “ An Introduction to Orthogonal Polynomials ” . New York : Gordon and Breach .
   Google Scholar
• Dattoli , G. and Ricci , P. E. 2003 . Laguerre-type exponentials, and the relevant L-circular and L-hyperbolic functions . Georgian Math. J. , 10 : 481 – 494 .
   Google Scholar
• Hahn , W. 1935 . Über die Jacobischen polynome und zwei verwandte polynomklassen . Math. Z , 39 : 634 – 638 . (doi:10.1007/BF01201380)
   Google Scholar
• Hochstadt , H. 1971 . “ The Functions of Mathematical Physics ” . New York : Dover Publications Inc .
   Google Scholar
• Koornwinder , T. 2006 . “ Lowering and raising operators for some special orthogonal polynomials ” . In Jack, Hall-Littlewood and Macdonald Polynomials , Edited by: Kuznetsov , V. B. and Sahi , S. 227 – 238 . Providence, RI : Contemporary Mathematics 417, American Mathematical Society .
   Google Scholar
• Loureiro , A. F. 2008 . Hahn's generalised problem and corresponding Appell polynomial sequences Doctoral Dissertation, Universidade de Porto
   Google Scholar
• Loureiro , A. F. and Maroni , P. 2008 . Quadratic decomposition of Appell sequences . Expo. Math. , 26 : 177 – 186 . (doi:10.1016/j.exmath.2007.10.002)
   Web of Science ®Google Scholar
• P. Maroni, Une théorie algébrique des polynômes orthogonaux Applications aux polynômes orthogonaux semi-classiques, in Orthogonal Polynomials and Their Applications, C. Brezinski, L. Gori, and A. Ronveaux, eds., IMACS Ann. Comput. Appl. Math. 9 (1991), pp. 95–130.
   Google Scholar
• P. Maroni, Fonctions Eulériennes, Polynômes Orthogonaux Classiques, Techniques de l'Ingénieur, Traité Généralités (Sciences Fondamentales) Vol. A 154, Paris, 1994, pp. 1–30.
   Google Scholar