<p>In this paper, we give two new <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1162_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$A_n$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> WP–Bailey lattices which are different from the result in “A <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1162_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">$U(n+1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> WP–Bailey lattice and its applications, Ramanujan J 46(2): 403–429, 2018.” By iterating the lattices, we obtain some new transformations and summations of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1162_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$A_n$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> basic hypergeometric series. By inserting unit WP–Bailey pairs to WP–Bailey lattices, we obtain a series of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1162_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$A_n$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>A</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> extensions of transformations <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1162_Article_IEq7.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$_{10}\phi _9$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mn>10</mn> <mrow /> </mmultiscripts> <msub> <mi>ϕ</mi> <mn>9</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1162_Article_IEq8.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$_8\phi _7$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mn>8</mn> <mrow /> </mmultiscripts> <msub> <mi>ϕ</mi> <mn>7</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>.</p>

Two WP–Bailey lattices over the root system $A_n$ and their applications

期刊论文
发表日期：

2025年7月21日

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Pei Gao

摘要

In this paper, we give two new $A_n$ $A_{n}$ WP–Bailey lattices which are different from the result in “A $U(n+1)$ $U (n + 1)$ WP–Bailey lattice and its applications, Ramanujan J 46(2): 403–429, 2018.” By iterating the lattices, we obtain some new transformations and summations of $A_n$ $A_{n}$ basic hypergeometric series. By inserting unit WP–Bailey pairs to WP–Bailey lattices, we obtain a series of $A_n$ $A_{n}$ extensions of transformations $_{10}\phi _9$ $_{10} ϕ_{9}$ to $_8\phi _7$ $_{8} ϕ_{7}$ .

Two WP–Bailey lattices over the root system \(A_n\) and their applications

摘要