{"title":"NEW CONGRUENCES FOR THE TRUNCATED APPELL SERIES","authors":"XIAOXIA WANG, WENJIE YU","doi":"10.1017/s0004972724000236","DOIUrl":null,"url":null,"abstract":"<p>Liu [‘Supercongruences for truncated Appell series’, <span>Colloq. Math.</span> <span>158</span>(2) (2019), 255–263] and Lin and Liu [‘Congruences for the truncated Appell series <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240417092342642-0507:S0004972724000236:S0004972724000236_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$F_3$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240417092342642-0507:S0004972724000236:S0004972724000236_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$F_4$</span></span></img></span></span>’, <span>Integral Transforms Spec. Funct.</span> <span>31</span>(1) (2020), 10–17] confirmed four supercongruences for truncated Appell series. Motivated by their work, we give a new supercongruence for the truncated Appell series <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240417092342642-0507:S0004972724000236:S0004972724000236_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$F_{1}$</span></span></img></span></span>, together with two generalisations of this supercongruence, by establishing its <span>q</span>-analogues.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0004972724000236","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Liu [‘Supercongruences for truncated Appell series’, Colloq. Math.158(2) (2019), 255–263] and Lin and Liu [‘Congruences for the truncated Appell series $F_3$ and $F_4$’, Integral Transforms Spec. Funct.31(1) (2020), 10–17] confirmed four supercongruences for truncated Appell series. Motivated by their work, we give a new supercongruence for the truncated Appell series $F_{1}$, together with two generalisations of this supercongruence, by establishing its q-analogues.
Liu ['Supercongruences for truncated Appell series', Colloq.Math.158(2) (2019), 255-263] and Lin and Liu ['Congruences for the truncated Appell series $F_3$ and $F_4$', Integral Transforms Spec.Funct.31(1) (2020), 10-17] 确认了截断阿贝尔数列的四个超级共轭。受他们工作的启发，我们给出了截断阿贝尔数列 $F_{1}$ 的新超共假，并通过建立其 q-analogues ，给出了该超共假的两个广义。
$F_3$ and 
$F_4$’, Integral Transforms Spec. Funct. 31(1) (2020), 10–17] confirmed four supercongruences for truncated Appell series. Motivated by their work, we give a new supercongruence for the truncated Appell series 
$F_{1}$, together with two generalisations of this supercongruence, by establishing its q-analogues.
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