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Keywords = generalized Bernoulli polynomials and numbers attached to a Dirichlet character χ

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10 pages, 255 KB  
Article
Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ
by Serkan Araci, Waseem Ahmad Khan and Kottakkaran Sooppy Nisar
Symmetry 2018, 10(12), 675; https://doi.org/10.3390/sym10120675 - 29 Nov 2018
Cited by 4 | Viewed by 2787
Abstract
We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on Z p . The results presented here, [...] Read more.
We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on Z p . The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)
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