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<p>In this paper, we calculate the centroid of the zeroes of semi-classical orthogonal polynomials of class one, which are derived from cubic decompositions (CD) satisfying the relation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W_{3n}(x) = P_n(x^{3} + q x + r)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>W</mi> <mrow> <mn>3</mn> <mi>n</mi> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mn>3</mn> </msup> <mo>+</mo> <mi>q</mi> <mi>x</mi> <mo>+</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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New findings on zero centroids in semi-classical orthogonal polynomials of class one

  • 期刊论文

  • 发表日期：

    2025年11月29日

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  • Jihad Souissi

摘要

In this paper, we calculate the centroid of the zeroes of semi-classical orthogonal polynomials of class one, which are derived from cubic decompositions (CD) satisfying the relation \(W_{3n}(x) = P_n(x^{3} + q x + r)\) W 3 n ( x ) = P n ( x 3 + q x + r ) .