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<p>In this paper, we derive several <i>q</i>-supercongruences, including a new one-parameter generalization of Van Hamme’s noted (B.2) supercongruence. Our approach employs Jackson’s <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1980_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(_6\phi _5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mn>6</mn> <mrow /> </mmultiscripts> <msub> <mi>ϕ</mi> <mn>5</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> summation formula combined with the creative microscoping technique pioneered by Guo and Zudilin (2019).</p>

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A q-generalization of Van Hamme’s (B.2) supercongruence

  • 期刊论文

  • 发表日期：

    2025年10月9日

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  • Chenying Wang,
  • Xuesong Cui

摘要

In this paper, we derive several q-supercongruences, including a new one-parameter generalization of Van Hamme’s noted (B.2) supercongruence. Our approach employs Jackson’s \(_6\phi _5\) 6 ϕ 5 summation formula combined with the creative microscoping technique pioneered by Guo and Zudilin (2019).