Results 11 to 20 of about 726,471 (254)
Bernoulli F-polynomials and Fibo–Bernoulli matrices [PDF]
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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Bernoulli Basis and the Product of Several Bernoulli Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We develop methods for computing the product of several Bernoulli and Euler polynomials by using Bernoulli basis for the vector space of polynomials of degree less than or equal to n.
Dae San Kim, Taekyun Kim
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FAULHABER POLYNOMIALS AND RECIPROCAL BERNOULLI POLYNOMIALS [PDF]
Rocky Mountain Journal of Mathematics, 2021 About four centuries ago, Johann Faulhaber developed formulas for the power sum $1^n + 2^n + \cdots + m^n$ in terms of $m(m+1)/2$. The resulting polynomials are called the Faulhaber polynomials.
Bernd C. Kellner
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Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials [PDF]
Mathematics, 2023 In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and ...
Dionisio Peralta +2 more
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Old and New Identities for Bernoulli Polynomials via Fourier Series [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of ...
Luis M. Navas +2 more
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Lagrange-Based Hypergeometric Bernoulli Polynomials
Symmetry, 2022 Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this paper,
Sahar Albosaily +3 more
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Degenerate poly type 2-Bernoulli polynomials [PDF]
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 ...
S. Araci
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Identities on the Bernoulli and Genocchi Numbers and Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We give some interesting identities on the Bernoulli numbers and polynomials, on the Genocchi numbers and polynomials by using symmetric properties of the Bernoulli and Genocchi polynomials.
Seog-Hoon Rim +2 more
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A Note on Symmetric Properties of the Twisted q-Bernoulli Polynomials and the Twisted Generalized q-Bernoulli Polynomials [PDF]
Advances in Difference Equations, 2010 We define the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomials attached to χ of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain
L.-C. Jang +5 more
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p-Bernoulli and geometric polynomials
International Journal of Number Theory, 2018 We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials. These results yield new identities for Bernoulli numbers. Moreover, we evaluate a Faulhaber-type summation in terms of [Formula: see text]-Bernoulli polynomials ...
Levent Kargın
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