Abstract
The properties of orthogonal polynomials and their associated polynomials can be used in the theory of Padé approximants and we can refind some classical results.
In the square blocks as well as an the northern and western sides we have identical Padé approximants above the principal antidiagonal of the square block P.
Especially in the case of the linear functionals lacunary of order 2, (in particular in the case of the Legendre and Tchebicheff orthogonal polynomials and their adjacent system of orthogonal polynomials) we can give some results of convergence for the corresponding Padé approximants (cf. [7]) in using some convergence results of the non commutative continued fractions.
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Draux, A. (1985). Orthogonal polynomials with respect to a linear functional lacunary of order S+1 in a non-commutative algebra. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076533
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DOI: https://doi.org/10.1007/BFb0076533
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