Some New Formulae for Genocchi Numbers and Polynomials Involving Bernoulli and Euler Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2014 We give some new formulae for product of two Genocchi polynomials including Euler polynomials and Bernoulli polynomials. Moreover, we derive some applications for Genocchi polynomials to study a matrix formulation.
Serkan Araci +2 more
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Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials [PDF]
MathematicsWe extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials.
Paolo Emilio Ricci +2 more
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Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol–Bernoulli Polynomials and Numbers, and Degenerate Apostol–Euler Polynomials and Numbers [PDF]
Axioms, 2022 In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Faà di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for Fubini-type ...
Siqintuya Jin +2 more
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Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 Let Pn={p(x)∈ℝ[x]∣deg p(x)≤n} be an inner product space with the inner product 〈p(x),q(x)〉=∫0∞xαe-xp(x)q(x)dx, where p(x),q(x)∈Pn and α∈ℝ with α>-1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis
Taekyun Kim, Dae San Kim
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Some Identities on Laguerre Polynomials in Connection with Bernoulli and Euler Numbers [PDF]
Discrete Dynamics in Nature and Society, 2012 We study some interesting identities and properties of Laguerre polynomials in connection with Bernoulli and Euler numbers. These identities are derived from the orthogonality of Laguerre polynomials with respect to inner product ∫⟨𝑓,𝑔⟩=∞0𝑒−𝑥2𝑓(𝑥)𝑔(𝑥)𝑑𝑥.
Dae San Kim +2 more
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Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials [PDF]
, 2002 In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are ...
Luo, Qiu-Ming, Qi, Feng
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Anharmonic Polynomial Generalizations of the Numbers of Bernoulli and Euler [PDF]
Transactions of the American Mathematical Society, 1922 We consider twelve infinite systems of polynomials in z which for z = 1 degenerate either to the numbers of Bernoulli or Euler, or to others simply dependent upon these. The first part proceeds from the definition of anharmonic polynomials to the specific twelve systems discussed; the second presents an adaptation of the symbolic calculus of Blissard ...
E. T. Bell
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Explicit formulas for Euler polynomials and Bernoulli numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In this paper, we give several explicit formulas involving the n-th Euler polynomial E_{n}\left(x\right). For any fixed integer m\geq n, the obtained formulas follow by proving that E_{n}\left(x\right) can be written as a linear combination of the polynomials x^{n}, \left(x+r\right)^{n},\ldots, \left(x+rm\right)^{n}, with r\in \left \{1,-1,\frac{1}{2 ...
Laala Khaldi +2 more
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Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory [PDF]
Symmetry, 2023 Bernoulli and Euler numbers and polynomials are well known and find applications in various areas of mathematics, such as number theory, combinatorial mathematics, series expansions, and the theory of special functions. Using fractional exponential functions, we extend the classical Bernoulli and Euler numbers and polynomials to introduce their ...
Diego Caratelli +2 more
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Explicit Formulas Involving -Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator.
Serkan Araci +2 more
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