{"title":"包含奇调和数的组合和、级数和积分","authors":"Kunle Adegoke, Robert Frontczak, Taras Goy","doi":"10.1007/s13370-025-01346-1","DOIUrl":null,"url":null,"abstract":"<div><p>We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combinatorial sums, series and integrals involving odd harmonic numbers\",\"authors\":\"Kunle Adegoke, Robert Frontczak, Taras Goy\",\"doi\":\"10.1007/s13370-025-01346-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 3\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-06-28\",\"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/s13370-025-01346-1\",\"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/s13370-025-01346-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Combinatorial sums, series and integrals involving odd harmonic numbers
We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers.
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