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The symmetric D ω -semi-classical orthogonal polynomials of class one

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Abstract

We give the system of Laguerre–Freud equations associated with the D ω -semi-classical functionals of class one, where D ω is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases. The corresponding integral representations are given.

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References

  1. Abdelkarim, F., Maroni, P.: The D ω -classical orthogonal polynomials. Result. Math. 32, 1–28 (1997)

    MATH  MathSciNet  Google Scholar 

  2. Alaya, J., Maroni, P.: Symmetric Laguerre–Hahn forms of class s=1. Integral Transforms Spec. Funct. 4, 301–320 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Askey, R., Wilson, J.: A set of hypergeometric orthogonal polynomials. SIAM J. Math. Anal. 13, 651–655 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  4. Askey, R., Wilson, J.: Some Basic Hypergeomertic Orthogonal Polynomials that Generalize Jacobi Polynomials. Memoirs of the American Mathematical Society 319. Providence, Rhole Island (1985)

  5. Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, New York (1978)

    MATH  Google Scholar 

  6. Bachène, M.: Les polynômes semi-classiques de classe zéro et de classe un. Thesis of third cycle, Univ. P. and M. Curie, Paris (1985)

  7. Belmehdi, S.: On semi-classical linear functional of class s=1. Classification and integral representations. Indag. Math. 3, 253–275 (1992)

    MATH  MathSciNet  Google Scholar 

  8. Foupouagnigni, M., Hounkonnou, M.N., Ronveaux, A.: Laguerre–Freud equations for the recurrence coefficients of D ω -semi-classical orthogonal polynomials of class one. J. Comp. Appl. Math. 99, 143–154 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. Koekoek, R., Swarttow, R.F.: The ASkey-scheme of hypergeometric orthogonal polynomials and its q-analogue. Report 98–17, TU Delft (1998)

  10. Marcellan, F., Salto, L.: Discrete semi-classical orthogonal polynomials. J. Differ. Equ. Appl. 4, 463–490 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Maroni, P.: Variations around classical orthogonal polynomials. Connected problems. J. Comp. Appl. Math. 48, 133–155 (1993)

    MATH  MathSciNet  Google Scholar 

  12. Ronveaux, A.: Discrete semi-classical orthogonal polynomials: generalized Meixner polynomials. J. Approx. Theory 46(4), 403–407 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. Stieltjes, T.J.: Recherche sur les fractions continues. Ann. Fac. Sci. Toulouse 8, J1–122 (1894); 9, A 1–47 (1895)

    MathSciNet  Google Scholar 

  14. Van Assche, W., Foupouagnigni, M.: Analysis of non-linear recurrence relations for the recurrence coefficients of generalized Charlier polynomials. J. Nonlin. Math. Phys. 10 (Suppl. 2), 231–237 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Centre National de la Recherche Scientifique (CNRS), Boite courrier 187, 75252, Paris cedex05, France

    P. Maroni

  2. Institut Supérieur des Sciences Appliquées et de Technologie, Rue Omar Ibn El Khattab, Gabes, 6072, Tunisia

    M. Mejri

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  1. P. Maroni
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  2. M. Mejri
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Correspondence to M. Mejri.

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In memory of Professor Luigi Gatteschi.

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Maroni, P., Mejri, M. The symmetric D ω -semi-classical orthogonal polynomials of class one. Numer Algor 49, 251–282 (2008). https://doi.org/10.1007/s11075-008-9170-2

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  • DOI: https://doi.org/10.1007/s11075-008-9170-2

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