{"title":"通过梅林变换得到的几个经典恒等式","authors":"Khristo N. Boyadzhiev","doi":"10.20948/mathmontis-2022-55-1","DOIUrl":null,"url":null,"abstract":"We present a summation rule using Mellin’s transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative integers are expressed in terms of Bernoulli polynomials. We also show identities involving exponential and Hermite polynomials.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"5 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Several classical identities via Mellin’s transform\",\"authors\":\"Khristo N. Boyadzhiev\",\"doi\":\"10.20948/mathmontis-2022-55-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a summation rule using Mellin’s transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative integers are expressed in terms of Bernoulli polynomials. We also show identities involving exponential and Hermite polynomials.\",\"PeriodicalId\":170315,\"journal\":{\"name\":\"Mathematica Montisnigri\",\"volume\":\"5 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Montisnigri\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.20948/mathmontis-2022-55-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Montisnigri","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20948/mathmontis-2022-55-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Several classical identities via Mellin’s transform
We present a summation rule using Mellin’s transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative integers are expressed in terms of Bernoulli polynomials. We also show identities involving exponential and Hermite polynomials.
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