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<p>In this work, we address the problem of expressing sequences of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>d</mi> </math></EquationSource> <EquationSource Format="TEX">$d$</EquationSource> </InlineEquation>-orthogonal polynomials in terms of either orthogonal polynomials or the canonical basis. We derive a general recurrence relation that enables the symbolic recursive computation of these coefficients. Several results are established to investigate the impact of the Appell character, as well as the symmetry and <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>d</mi> </math></EquationSource> <EquationSource Format="TEX">$d$</EquationSource> </InlineEquation>-symmetry of the polynomial sequences, on these coefficients. Additionally, we deduce some results concerning the zeros of <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <mi>d</mi> </math></EquationSource> <EquationSource Format="TEX">$d$</EquationSource> </InlineEquation>-orthogonal polynomials.</p>

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On Connection Coefficients of \(d\)-Orthogonal Polynomials in Terms of Orthogonal Polynomials and the Canonical Basis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月14日

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  • Teresa A. Mesquita,
  • Zélia da Rocha

摘要

In this work, we address the problem of expressing sequences of d $d$ -orthogonal polynomials in terms of either orthogonal polynomials or the canonical basis. We derive a general recurrence relation that enables the symbolic recursive computation of these coefficients. Several results are established to investigate the impact of the Appell character, as well as the symmetry and d $d$ -symmetry of the polynomial sequences, on these coefficients. Additionally, we deduce some results concerning the zeros of d $d$ -orthogonal polynomials.