Abstract
We deal with the 2‐orthogonal, 2‐symmetric self‐associated sequence (2‐orthogonal Tchebychev polynomials) and its cubic components. We prove that all the forms (linear functionals) arising are third degree forms. Therefore, an introduction to third degree forms is provided. We look for the connection between these components which are 2‐orthogonal with respect to the functional vector t(w0{μ},w1 μ) and orthogonal sequences with respect to w0 μ, μ=0,1,2. Associated forms w0 μ)1) and their inverse w0 μ)-1 are also studied through the symmetrized w0}0 μ, μ=0,1,2. Further, we give integral representations for some of these forms.
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Ben Salah, I., Maroni, P. The connection between self‐associated two‐dimensional vector functionals and third degree forms. Advances in Computational Mathematics 13, 51–77 (2000). https://doi.org/10.1023/A:1018941924408
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DOI: https://doi.org/10.1023/A:1018941924408