{"title":"多重斐波那契函数的解析延拓","authors":"S. S. Rout, N. K. Meher","doi":"10.3792/PJAA.94.64","DOIUrl":null,"url":null,"abstract":": In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Analytic continuation of the multiple Fibonacci zeta functions\",\"authors\":\"S. S. Rout, N. K. Meher\",\"doi\":\"10.3792/PJAA.94.64\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3792/PJAA.94.64\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/PJAA.94.64","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
摘要
在本文中,我们证明了深度为2的多个Fibonacci zeta函数的亚纯延拓,其中fn是第n个Fibonacci数,Re ð s 1 Þ > 0, Re ð s 2 Þ > 0。我们计算了它的极点及其残数的完整列表。我们也证明了多个Fibonacci zeta值在负整数参数上是有理数。
Analytic continuation of the multiple Fibonacci zeta functions
: In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.