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<p>We analyze the algebraic structure of higher order ladder operators for classical orthogonal polynomials (Hermite, Laguerre, Jacobi, Bessel) in terms of their moment functionals and two first order ladder operators, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3245_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(J_n^+\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>J</mi> <mi>n</mi> <mo>+</mo> </msubsup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3245_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(J_n^-\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>J</mi> <mi>n</mi> <mo>-</mo> </msubsup> </math></EquationSource> </InlineEquation>. We study operational expressions for these ladder operators in terms of certain integro-differential operators.</p>

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On higher order ladder operators for classical orthogonal polynomials

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Misael E. Marriaga,
  • Javier Martínez

摘要

We analyze the algebraic structure of higher order ladder operators for classical orthogonal polynomials (Hermite, Laguerre, Jacobi, Bessel) in terms of their moment functionals and two first order ladder operators, \(J_n^+\) J n + and \(J_n^-\) J n - . We study operational expressions for these ladder operators in terms of certain integro-differential operators.