3.8 Article

SYMBOLIC APPROACH TO THE GENERAL CUBIC DECOMPOSITION OF POLYNOMIAL SEQUENCES. RESULTS FOR SEVERAL ORTHOGONAL AND SYMMETRIC CASES

Journal

OPUSCULA MATHEMATICA
Volume 32, Issue 4, Pages 675-687

Publisher

AGH UNIV SCIENCE & TECHNOLOGY PRESS
DOI: 10.7494/OpMath.2012.32.4.675

Keywords

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

Funding

  1. FCT (Portugal)
  2. Program POPH/FSE
  3. European Regional Development Fund through the programme COMPETE
  4. Portuguese Government through the FCT Fundacao para a Ciencia e a Tecnologia [PEst-C/MAT/UI0144/2011]

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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.

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