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General quadratic decomposition

2010; Taylor & Francis; Volume: 16; Issue: 11 Linguagem: Inglês

10.1080/10236190902810393

1563-5120

Ângela Macedo, P. Maroni,

Advanced Mathematical Theories and Applications

Abstract A general quadratic decomposition of polynomial sequences is carried out. This generalizes the works of L. Carlitz, Boll. Un. Mat. Ital. 16 (1961), pp. 386–390; L.M. Chihara and T.S. Chihara, J. Math. Anal. Appl. 126 (1987), pp. 275–291; T.S. Chihara, Boll. Un. Mat. Ital. 19 (1964), pp. 451–459 and that of P. Maroni, Rev. Math. Pura ed Appl. (6) (1990), pp. 19–53. We deal with the transformation , where instead of that where p and q are zero. We give the general quadratic decomposition of a monic polynomial sequence. The characterization of the cases where is orthogonal are given. Keywords: orthogonal polynomialsquadratic decompositionmonic polynomial sequence (MPS)monic orthogonal polynomial sequence (MOPS)2000 Mathematics Subject Classification:: 42C0533C45 Acknowledgements Â. Macedo has been supported by the PRODEP III Concurso no 4/2000 Acção 5.3 – Doutoramento, and also wishes to thank Universidade de Trás-os-Montes e Alto Douro. Part of this work was performed while P. Maroni was in residence at the Departamento de Matemática Aplicada of Faculdade de Ciências da Universidade do Porto. He is grateful for the support of the Fundação para a Ciência e Tecnologia, PRAXIS XXI.