Results 11 to 20 of about 15,530 (193)
Symmetry, 2023 Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with the help of generating functions and their functional equations. In this paper, we define the generalized (p,q)-Bernoulli–Fibonacci and generalized (p,q)-Bernoulli–Lucas polynomials and numbers by using ...
Hao Guan +2 more
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Axioms, 2022 In this paper, we focus on the higher-order derivatives of the hyperharmonic polynomials, which are a generalization of the ordinary harmonic numbers. We determine the hyperharmonic polynomials and their successive derivatives in terms of the r-Stirling ...
José L. Cereceda
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A Study on Generalized Degenerate Form of 2D Appell Polynomials via Fractional Operators
Fractal and Fractional, 2023 This paper investigates the significance of generating expressions, operational principles, and defining characteristics in the study and development of special polynomials.
Mohra Zayed, Shahid Ahmad Wani
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Generalized Mixed Type Bernoulli-Gegenbauer Polynomials
Kragujevac Journal of Mathematics, 2023 The generalized mixed type Bernoulli-Gegenbauer polynomials of order α >−1/2 are special polynomials obtained by use of the generating function method. These polynomials represent an interesting mixture between two classes of special functions, namely generalized Bernoulli polynomials and Gegenbauer polynomials.
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Bernoulli F-polynomials and Fibo–Bernoulli matrices
Advances in Difference Equations, 2019 In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
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Identity for generalized Bernoulli polynomials
, 2020 In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.
Chellal, Redha +2 more
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Generalized q-Bernoulli Polynomials Generated by Jackson q-Bessel Functions
Results in Mathematics, 2022 AbstractIn this paper, we introduce the polynomials $$B^{(k)}_{n,\alpha }(x;q)$$ B n , α ( k
S. Z. H. Eweis, Z. S. I. Mansour
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Karpatsʹkì Matematičnì Publìkacìï, 2022 The aim of this paper is to study new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order $\alpha$ and level $m$ in the variable $x$. Here the degenerate polynomials are a natural extension of the
W. Ramírez, C. Cesarano
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The Lazard formal group, universal congruences and special values of zeta functions [PDF]
, 2015 A connection between the theory of formal groups and arithmetic number theory is established. In particular, it is shown how to construct general Almkvist--Meurman--type congruences for the universal Bernoulli polynomials that are related with the Lazard
Tempesta, Piergiulio
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Extended Bernoulli and Stirling matrices and related combinatorial identities [PDF]
, 2013 In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli and Stirling numbers of both kinds. These formulas are deduced from Pascal type matrix representations of Bernoulli and Stirling numbers ...
Can, Mümün, Dağlı, M. Cihat
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