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Integral Transforms and Special Functions Volume 14, 2003 - Issue 1
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Original Articles

\Delta -Coherent Pairs and Orthogonal Polynomials of a Discrete Variable

I. Area Departamento de Matemática Aplicada, E.T.S.I. Industriales y Minas, Universidad de Vigo, Campus Lagoas-Marcosende, Vigo, 36200, Spain
,
E. Godoy Departamento de Matemática Aplicada, E.T.S.I. Industriales y Minas, Universidad de Vigo, Campus Lagoas-Marcosende, Vigo, 36200, Spain
&
F. MarcellÁn Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, Avenida de la Universidad, 30, Leganés, 28911, Madrid, Spain
Pages 31-57 | Published online: 18 Oct 2010

  • Abdelkarim , F. and Maroni , P. 1997 . The D?-classical orthogonal polynomials . Result. Math. , 32 : 1 – 28 .
  • Abramowitz , M. and Stegun , I. 1965 . Handbook of Mathematical Functions , New York : Dover .
  • Álvarez-Nodarse , R. and Marcellan , F. 1995 . The modification of classical Hahn polynomials of a discrete variable . Integral Transforms and Special Functions , 4 (3) : 243 – 262 .
  • Álvarez-Nodarse , R. , Garcia , A. G. and Marcellan , F. 1995 . On the properties for modifications of classical orthogonal polynomials of discrete variables . J. Comput. Appl. Math. , 65 : 3 – 18 .
  • Area , I. , Godoy , E. and Marcellan , F. 2000 . Classification of all ?-coherent pairs . Integral Transforms and Special Functions , 9 (1) : 1 – 18 .
  • Chihara , T. S. 1978 . An Introduction to Orthogonal Polynomials , New York : Gordon and Breach .
  • Garc?a , A. G. , Marcellán , F. and Salto , L. 1995 . A distributional study of discrete classical orthogonal polynomials . J. Comput. Appl Math. , 57 : 147 – 162 .
  • Gautschi , W. 1982 . “ An algorithmic implementation of the generalized Christoffel theorem ” . In Numerical Integration. Proceedings of the Conference 1981 Held at the Mathematisches Forschungsinstitut Oberwolfach, October 4-10 , International Series of Numerical Mathematics Edited by: Hämmerlin , G. Vol. 57 , 89 – 106 . Basel-BostonStuttgart : Birkhäuser Verlag .
  • series , A. , Koch , P. E. , Nersett , S. P. and Sanz-Serna , J.M . 1991 . On Polynomials orthogonal with respect tocertain Sobolev Inner Products . J. Approx. Theory , 65 : 151 – 175 .
  • Koekoek , R. and Swarttouw , R. F. 1998 . The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report 98-17, Fac. Techn. Math , Delft : Informatics, Delft University of Technology .
  • Lesley , P. A. 1995 . Vervollständigung der klassischen Orthogonalpolynome durch Ergänzungen zum Askey-Schema der hypergeometrischen orthogonalen Polynome . Sitzungsber. Abt. , 11 : 204 151 – 166 .
  • Levenshtein , V. I. 1995 . Krawtchouk polynomials and universal bounds for codes and design in Hammingspaces . IEEE Trans. Inform. Theory , 41 : 1303 – 1321 .
  • Marcellán , F. and Maroni , P. 1992 . Sur l'adjonction d'une masse de Dirac á une forme régulière et semiclassique . Ann. Mat. Para ed Appl. , CLXII (IV) : 1 – 22 .
  • Marcellán , F. , Martínez-Finkelshtein , A. and Moreno-Balcazar , J. J. 1997 . Asymptotics of Sobolev orthogonalpolynomials for symmetrically coherent pairs of measures with compact support . J. Comput. Appl. Math. , 81 (2) : 217 – 227 .
  • Marcellán , F. and Petronilho , J. C. 1995 . Orthogonal polynomials and coherent pairs: the classical case . Indag.Mathem. N.S. , 6 (3) : 287 – 307 .
  • Marcellán , F. , Petronilho , J. C. , Pérez , T. E. and Piñar , M. A. 1995 . What is beyond coherent pairs oforthogonal polynomials? . J. Comput. Appl. Math. , 65 : 267 – 277 .
  • Marcellán , F. and Salto , L. 1998 . Discrete semi-classical orthogonal polynomials . J. Difference Equations , 4 : 463 – 496 .
  • Maroni , P. 1991 . “ Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonauxsemi-classiques ” . In Orthogonal Polynomials and TheirApplications , Edited by: Brezinski , C. , Gori , L. and Ronveaux , A. Vol. 9 , 95 – 130 . Basel, , Switzerland : J. C. Baltzer A. G .
  • Martínez-Finkelshtein , A. , Moreno Balcázar , J. J. , Pérez , T. E. and Piñar , M. A. 1998 . Asymptotics of Sobolevorthogonal polynomials for coherent pairs of measures . J. Approx. Theory , 92 (2) : 280 – 293 .
  • Meijer , H. G. 1997 . Determination of all coherent pairs . J. Approx. Theory , 89 : 321 – 343 .
  • Nikiforov , A. F. , Suslov , S. K. and Uvarov , V. B. 1991 . Classical Orthogonal Polynomials of a DiscreteVariable , Berlin : Springer-Verlag .
  • Pan , K. 1998 . Asymptotics for Sobolev orthogonal polynomials with coherent pairs: The Jacobi case . type I.Proc. Amer. Math. Soc. , 126 : 2377 – 2388 .
  • Pan , K. 1997 . On Sobolev orthogonal polynomials with coherent pairs . The Jacobi case. J. Compta Appl.Math. , 79 (2) : 249 – 262 .

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