{"title":"从 $${\\varvec{k}}$ k -Pell 序列获得的双曲函数","authors":"Bahar Kuloğlu, Engin Özkan","doi":"10.1007/s13370-023-01160-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, an expansion of the classical hyperbolic functions is presented and studied. Also, many features of the <span>\\(k-\\)</span> Pell hyperbolic functions are given. Finally, some graph and curved surfaces related to the k − Pell hyperbolic functions are introduced.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hyperbolic functions obtained from \\\\({\\\\varvec{k}}\\\\)-Pell sequences\",\"authors\":\"Bahar Kuloğlu, Engin Özkan\",\"doi\":\"10.1007/s13370-023-01160-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, an expansion of the classical hyperbolic functions is presented and studied. Also, many features of the <span>\\\\(k-\\\\)</span> Pell hyperbolic functions are given. Finally, some graph and curved surfaces related to the k − Pell hyperbolic functions are introduced.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-01-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-023-01160-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-023-01160-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文提出并研究了经典双曲函数的扩展。此外,还给出了 \(k-\) Pell 双曲函数的许多特征。最后,介绍了一些与 k - Pell 双曲函数相关的图形和曲面。
Hyperbolic functions obtained from \({\varvec{k}}\)-Pell sequences
In this paper, an expansion of the classical hyperbolic functions is presented and studied. Also, many features of the \(k-\) Pell hyperbolic functions are given. Finally, some graph and curved surfaces related to the k − Pell hyperbolic functions are introduced.