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<p>The present paper is devoted to three new special <i>q</i>-series transformation formulas which may serve as further applications of the paper (J. Difference Equ. Appl. 30(2024) 553–576). Further, by making use of these three special transformations and their <i>q</i>-difference equations, we establish the relevant <i>q</i>-contiguous relations for four kinds of finite <i>q</i>-series. Several new transformations including one for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({}_2\phi _1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> <msub> <mi>ϕ</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> series and another for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({}_4\phi _3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mn>4</mn> <mrow /> </mmultiscripts> <msub> <mi>ϕ</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> series are presented.</p>

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General q-series transformations based on Abel’s lemma on summation by parts and their applications -(II)

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Jianan Xu,
  • Xinrong Ma

摘要

The present paper is devoted to three new special q-series transformation formulas which may serve as further applications of the paper (J. Difference Equ. Appl. 30(2024) 553–576). Further, by making use of these three special transformations and their q-difference equations, we establish the relevant q-contiguous relations for four kinds of finite q-series. Several new transformations including one for \({}_2\phi _1\) 2 ϕ 1 series and another for \({}_4\phi _3\) 4 ϕ 3 series are presented.