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<p>In this paper, we extend the <i>q</i>-Dyson constant term identity by categorizing the variables into <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> parts. The original <i>q</i>-Dyson constant term identity corresponds to the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> case. Using Cai’s splitting approach, we establish a recursion for this constant term involving <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> components.</p>

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Recursions for Multi-Component Extensions of the q-Dyson Constant Term Identity

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Wenlong Jiang,
  • Suzhen Wen,
  • Yueming Zhong,
  • Yue Zhou

摘要

In this paper, we extend the q-Dyson constant term identity by categorizing the variables into \(p+1\) p + 1 parts. The original q-Dyson constant term identity corresponds to the \(p=0\) p = 0 case. Using Cai’s splitting approach, we establish a recursion for this constant term involving \(p+1\) p + 1 components.