95
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

A non-symmetric second-degree semi-classical form of class one

, &
Pages 149-159 | Received 28 Jan 2011, Accepted 27 Feb 2011, Published online: 20 Apr 2011

References

  • Alaya , J. and Maroni , P. 1996 . Symmetric Laguerre–Hahn forms of class s=1 . Integral Transforms Spec. Funct. , 4 : 301 – 320 .
  • Álvarez-Nodarse , R. , Arvesú , J. and Marcellán , F. 2004 . Modifications of quasi-definite linear functionals via addition of delta and derivatives of delta Dirac functions . Indag. Math. N.S. , 15 : 1 – 20 .
  • Bachène , M. 1985 . “ Les polynômes semi-classiques de classe zéro et de classe un ” . Paris : Université Pierre et Marie Curie . Thèse de Troisième Cycle
  • Beghdadi , D. 1995 . “ Sur quelques formes du second degré et leurs inverses ” . Paris : Université Pierre et Marie Curie . Thèse de l’
  • Beghdadi , D. 2000 . Second degree semi-classical forms of class s=1. The symmetric case . Appl. Numer. Math. , 34 : 1 – 11 .
  • Beghdadi , D. and Maroni , P. 1997 . Second degree classical forms . Indag. Math. N.S. , 8 : 439 – 452 .
  • Beghdadi , D. and Maroni , P. 1998 . On the inverse problem of the product of a semiclassical form by a polynomial . J. Comput. Appl. Math. , 88 : 377 – 399 .
  • Belmehdi , S. 1991 . “ On the left multiplication of a regular linear functional by a polynomial ” . In Orthogonal Polynomials and their Applications , Edited by: Brezinski , C. , Gori , L. and Ronveaux , A. 169 – 176 . Basel : AG Baltzer . IMACS Annals on Computing and Applied Mathematics, Vol. 9
  • Belmehdi , S. 1992 . On semi-classical linear functionals of class s=1. Classification and integral representation . Indag. Math. N.S. , 3 : 253 – 275 .
  • Bouras , B. and Alaya , A. 2007 . A large family of semi-classical polynomials of class one . Integral Transforms Spec. Funct. , 18 : 913 – 931 .
  • Chihara , T. S. 1978 . An Introduction to Orthogonal Polynomials , New York : Gordon and Breach .
  • Dini , J. and Maroni , P. 1989 . Sur la multiplication d'une forme semi-classique par un polynôme . Publ. Sem. Math. Univ. d'Antananarivo , 3 : 76 – 89 .
  • Dini , J. and Maroni , P. 1989 . The Product of a Linear Form by a Rational Fraction: Application to Laguerre-Hahn Forms , 131 – 138 . New York : M. Dekker . Lect. Notes in Pure and Appl. Math., Vol. 117
  • Marcellán , F. and Prianes , E. Orthogonal polynomials and linear functionals of second degree . Proceedings 3rd International Conference on Approximation and Optimization . Edited by: Bank , B. , Bustamante , J. , Guddat , J. , Jimenez , M. A. , Jongen , H. Th. and Römisch , W. pp. 149 – 162 . México : Sociedad Matemática Mexicana . Aportaciones Matemáticas, Serie Comunicaciones, Vol. 24
  • Maroni , P. 1988 . “ Le calcul des formes linéaires et les polynômes orthogonaux semi-classiques ” . In Orthogonal Polynomials and Their Applications , Edited by: Alfaro , M. , Dehesa , J. S. , Marcellán , F. J. , Rubio de Francia , J. L. and Vinuesa , J. 279 – 290 . Berlin : Springer . Lecture Notes in Mathematics, Vol. 1329
  • Maroni , P. 1990 . Sur la décomposition quadratique d'une suite de polynômes orthogonaux . I. Rivista di Mat. Pura ed Appl. , 6 : 19 – 53 .
  • Maroni , P. 1990 . Sur la suite de polynômes orthogonaux associée à la forme . Period. Math. Hungar. , 21 : 223 – 248 .
  • Maroni , P. 1991 . “ Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonaux semiclassiques ” . In Orthogonal Polynomials and their Applications , Edited by: Brezinski , C. , Gori , L. and Ronveaux , A. Vol. 9 , 95 – 130 . Basel : AG Baltzer . IMACS Annals on Computing and Applied Mathematics
  • Maroni , P. 1994 . Fonctions eulériennes. Polynômes orthogonaux classiques . Techniques de l'ingénieur, A , 154 : 1 – 30 .
  • Maroni , P. 1995 . Tchebychev forms and their perturbed as second degree forms . Ann. Numer. Math. , 2 : 123 – 143 .
  • Maroni , P. 1995 . An introduction to second degree forms . Adv. Comput. Math. , 3 : 59 – 88 .
  • Maroni , P. and Nicolau , I. 2003 . On the inverse problem of the product of a form by a polynomial: The cubic case . Appl. Numer. Math. , 45 : 419 – 451 .
  • Sansigre , G. and Valent , G. 1995 . A large family of semi-classical polynomials: the perturbed Tchebychev . J. Comput. Appl. Math. , 57 : 271 – 281 .
  • Sghaier , M. and Alaya , J. 2004 . Orthogonal polynomials associated with some modifications of a linear form . Methods Appl. Anal. , 11 : 267 – 294 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.