Quadratic decomposition of a Laguerre-Hahn polynomial sequence I
Copyright policy )Quadratic decomposition of a Laguerre-Hahn polynomial sequence I
Let \(P_n\) and \(B_n\) be sequences of monic orthogonal polynomials such that \(B_{2n}(x)=P_n(x^2)\) for all \(n\geq0\). In the present paper, the authors prove that, if one of the sequences is a Laguerre-Hahn orthogonal polynomial sequence, then so is the other. Moreover, they show the relation between the classes of such sequences and their corresponding structure relations.
recurrence coefficients, 42C05, Orthogonal polynomials, quadratic decomposition, Laguerre-Hahn polynomials, Laguerre-Hahn orthogonal polynomials, structure relation, structure relation coefficients, symmetric linear functionals, 33C45, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), three term recurrence relation, orthogonal polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
recurrence coefficients, 42C05, Orthogonal polynomials, quadratic decomposition, Laguerre-Hahn polynomials, Laguerre-Hahn orthogonal polynomials, structure relation, structure relation coefficients, symmetric linear functionals, 33C45, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), three term recurrence relation, orthogonal polynomials, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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