Opuscula Math. 32, no. 4 (2012), 675-687
http://dx.doi.org/10.7494/OpMath.2012.32.4.675
Opuscula Mathematica
Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases
Teresa A. Mesquita
Z. Da Rocha
Abstract. 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.
Keywords: symmetric polynomials, orthogonal polynomials, cubic decomposition, symbolic computations, Mathematica 8.0.1.0.
Mathematics Subject Classification: 33C45, 33D45, 42C05, 33F10, 68W30, 68-04.
- Teresa A. Mesquita
- ESTG - Instituto Superior Politécnico de Viana do Castelo & CMUP Av. do Atlântico, 4900-348 Viana do Castelo, Portugal
- Z. Da Rocha
- Departamento de Matemática - CMUP, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
- Received: 2011-05-28.
- Revised: 2012-01-28.
- Accepted: 2012-01-31.
