Results 31 to 40 of about 212 (165)
Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
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Construction of partially degenerate Laguerre–Bernoulli polynomials of the first kind
Applied Mathematics in Science and Engineering, 2022 In this paper, we introduce partially degenerate Laguerre–Bernoulli polynomials of the first kind and deduce some relevant properties by using a preliminary study of these polynomials.
Waseem A. Khan +2 more
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Degenerate Poly-Lah-Bell Polynomials and Numbers
Journal of Mathematics, 2022 Many mathematicians studied “poly” as a generalization of the well-known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly-Lah-Bell polynomials
Taekyun Kim, Hye Kyung Kim
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Some Identities of Degenerate Bell Polynomials
Mathematics, 2020 The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers.
Taekyun Kim +3 more
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A new approach to fully degenerate Bernoulli numbers and polynomials
Filomat, 2023 In this paper, we consider the doubly indexed sequence a(r) ? (n,m), (n,m ? 0), defined by a recurrence relation and an initial sequence a(r) ? (0,m), (m ? 0). We derive with the help of some differential operator an explicit expression for a(r) ?
Kim, Taekyun, Kim, Dae san
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Degenerate Poly-Type 2-Bernoulli Polynomials
Mathematical Sciences and Applications E-Notes, 2021 Recently, Kim-Kim [10] have studied type 2-Changhee and Daehee polynomials. They have also introduced the type 2-Bernoulli polynomials in order to express the central factorial numbers of the second kind by making use of type 2-Bernoulli numbers of negative integral orders. Inspired by their work, we consider a new class of generating functions of type
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A note on degenerate multi-poly-Bernoulli numbers and polynomials
Applicable Analysis and Discrete Mathematics, 2023 In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate some properties for those numbers and polynomials.
Kim, Taekyun, Kim, Dae San
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Advances in Difference Equations, 2019 In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 ...
Dae San Kim +3 more
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Hypergeometric degenerate Bernoulli polynomials and numbers
Ars Mathematica Contemporanea, 2020 Summary: Carlitz defined the degenerate Bernoulli polynomials \(\beta_n(\lambda,x)\) by means of the generating function \(t\left((1+\lambda t)^{1\lambda} -1\right)^{-1}(1+\lambda t)^{x/\lambda}\). In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli, Cauchy and Euler numbers.
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New degenerate Bernoulli, Euler, and Genocchi polynomials [PDF]
Pure Mathematics and Applications, 2020 Abstract We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function. Also, we present generalizations of some familiar identities and connection between these types of Bernoulli, Euler, and Genocchi polynomials.
Orli Herscovici, Toufik Mansour
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