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<p>We prove a kind of truncated basic hypergeometric series contain the factor <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2024_1816_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Phi _n(q)^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mi>n</mi> </msub> <msup> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2024_1816_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Phi _n(q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Φ</mi> <mi>n</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is the <i>n</i>-th cyclotomic polynomial. This generalizes a recent result of Cao, Guo and Yu.</p>

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Factors of a Kind of Truncated Basic Hypergeometric Series

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Long Li,
  • Su-Dan Wang

摘要

We prove a kind of truncated basic hypergeometric series contain the factor \(\Phi _n(q)^2\) Φ n ( q ) 2 , where \(\Phi _n(q)\) Φ n ( q ) is the n-th cyclotomic polynomial. This generalizes a recent result of Cao, Guo and Yu.