{"title":"A note on integral representation of some generalized zeta functions and its consequences","authors":"K. Mehrez","doi":"10.7153/MIA-2021-24-17","DOIUrl":null,"url":null,"abstract":". The main focus of the present note is to establish new integral representation for the Hurwitz-Lerch zeta and the multi-parameter Hurwitz-Lerch zeta functions. In particular, new integral expression of the polylogarithm function and the Fox-Wright function are derived. In addition, closed integral form expression of the moment generating function of a zeta distribution is established. As application, we derive the complete monotonicity properties of two classes of function related to the Hurwitz-Lerch zeta and the polylogarithm function. Moreover, some inequalities involving these two functions are proved.","PeriodicalId":49868,"journal":{"name":"Mathematical Inequalities & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Inequalities & Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/MIA-2021-24-17","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
. The main focus of the present note is to establish new integral representation for the Hurwitz-Lerch zeta and the multi-parameter Hurwitz-Lerch zeta functions. In particular, new integral expression of the polylogarithm function and the Fox-Wright function are derived. In addition, closed integral form expression of the moment generating function of a zeta distribution is established. As application, we derive the complete monotonicity properties of two classes of function related to the Hurwitz-Lerch zeta and the polylogarithm function. Moreover, some inequalities involving these two functions are proved.
期刊介绍：
''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.
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