{"title":"一类终止 $$_4\\phi _3$$ 序列的求和公式","authors":"Xu Yong, Wenlong Zhang","doi":"10.1007/s11139-024-00857-y","DOIUrl":null,"url":null,"abstract":"<p>In this paper we investigate a class of terminating <span>\\(_4\\phi _3\\)</span>-series. By utilizing the Carlitz inversion and four contiguous relations for the <span>\\(\\Omega _{\\lambda ,\\mu }\\)</span>-series, many new summation formulas for terminating <span>\\(_4\\phi _3\\)</span>-series are obtained.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Summation formulas for a class of terminating $$_4\\\\phi _3$$ -series\",\"authors\":\"Xu Yong, Wenlong Zhang\",\"doi\":\"10.1007/s11139-024-00857-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we investigate a class of terminating <span>\\\\(_4\\\\phi _3\\\\)</span>-series. By utilizing the Carlitz inversion and four contiguous relations for the <span>\\\\(\\\\Omega _{\\\\lambda ,\\\\mu }\\\\)</span>-series, many new summation formulas for terminating <span>\\\\(_4\\\\phi _3\\\\)</span>-series are obtained.</p>\",\"PeriodicalId\":501430,\"journal\":{\"name\":\"The Ramanujan Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Ramanujan Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-024-00857-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00857-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Summation formulas for a class of terminating $$_4\phi _3$$ -series
In this paper we investigate a class of terminating \(_4\phi _3\)-series. By utilizing the Carlitz inversion and four contiguous relations for the \(\Omega _{\lambda ,\mu }\)-series, many new summation formulas for terminating \(_4\phi _3\)-series are obtained.
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