{"title":"一些基本超几何函数的不等式","authors":"S. Kalmykov, D. Karp","doi":"10.15393/j3.art.2019.5210","DOIUrl":null,"url":null,"abstract":"We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur\\'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"41 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inequalities for some basic hypergeometric functions\",\"authors\":\"S. Kalmykov, D. Karp\",\"doi\":\"10.15393/j3.art.2019.5210\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur\\\\'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.\",\"PeriodicalId\":41813,\"journal\":{\"name\":\"Problemy Analiza-Issues of Analysis\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Problemy Analiza-Issues of Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15393/j3.art.2019.5210\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Problemy Analiza-Issues of Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15393/j3.art.2019.5210","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Inequalities for some basic hypergeometric functions
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur\'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.
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