Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases

• Autorzy: Mesquita T. A. , Rocha Z. Da
• Języki publikacji: EN

Abstrakty

EN

We deal with a symbolic approach to the cubic decomposition (CD) of polynomial sequences - presented in a previous article referenced herein - which allows us to compute explicitly the first elements of the nine component sequences of a CD. Properties are investigated and several experimental results are discussed, related to the CD of some widely known orthogonal sequences. Results concerning the symmetric character of the component sequences are established.

Słowa kluczowe

EN

symmetric polynomials; orthogonal polynomials; cubic decomposition; symbolic computations; Mathematica 8.0.1.0.

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 4
• Strony: 675--687
• Opis fizyczny: Bibliogr. 14, tab.

Twórcy

autor

Mesquita T. A.

autor

Rocha Z. Da

• ESTG – Instituto Superior Politécnico de Viana do Castelo & CMUP Av. do Atlântico, 4900-348 Viana do Castelo, Portugal,

Bibliografia

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• [3] W. Gautschi, Orthogonal polynomials: Computation and Approximation, Oxford University Press, Oxford, (2004).
• [4] W. Gautschi, Algorithm 726: ORTHPOL – A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules, ACM Trans. Math. Software, 20 (1994), 21–62.
• [5] W. Koepf, R. Swarttouw, CAOP: Computer Algebra and Orthogonal Polynomials, http://pool-serv1.mathematik.uni-kassel.de/CAOP
• [6] P. Maroni, Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonaux semi-classiques, [in:] C. Brezinski et al.; eds., Orthogonal Polynomials and their Applications, [in:] IMACS Ann. Comput. Appl. Math. 9 (Blatzer, Basel, 1991), 95–130.
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• [9] P. Maroni, T.A. Mesquita, Z. da Rocha, On the general cubic decomposition of polynomial sequences, J. Difference Equ. Appl. 17 (2011) 9, 1303–1332.
• [10] Z. da Rocha, Symbolic implementation, in the Mathematica language, for deriving closed formulas for connection coefficients between orthogonal polynomials, Preprints CMUP 7 (2010) 1–29, Centro de Matemática da Universidade do Porto, Portugal. http://cmup.fc.up.pt/cmup/v2/frames/publications.htm.
• [11] T.A. Mesquita, Z. da Rocha, Symbolic implementation of polynomial sequences cubic decomposition, Software CMUP, 1 (2012), Centro de Matemática da Universidade do Porto, Portugal. http://cmup.fc.up.pt/cmup/v2/frames/publications.htm
• [12] T.A. Mesquita, Polynomial Cubic Decomposition, Ph.D. Thesis, Universidade do Porto, Faculdade de Ciências, Departamento de Matemática, 2010.
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