Results 11 to 20 of about 1,563 (216)
Fully degenerate poly-Bernoulli numbers and polynomials
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
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On the 𝑞-Bernoulli Numbers and Polynomials with Weight 𝜶 [PDF]
Abstract and Applied Analysis, 2011 We present a systemic study of some families of higher-order 𝑞-Bernoulli numbers and polynomials with weight 𝛼. From these studies, we derive some interesting identities on the 𝑞-Bernoulli numbers and polynomials with weight 𝛼.
T. Kim, J. Choi
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Bernoulli Numbers and Polynomials via Residues [PDF]
Journal of Number Theory, 1999 In the ring \({\mathbb Q}[[T]]\) of formal power series the authors study the subring generated by \({\mathbb Q}, T\) and \(T/(e^T-1)\) together with the differential operator \(T(d/dT)\). Using their calculus of generalized fractions and residues they show that the Bernoulli numbers \(B^{(n)}_i\) of order \(n\) and Bernoulli polynomials \(B^{(n)}_i(X)\
Huang, I-Chiau, Huang, Su-Yun
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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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Congruences concerning Bernoulli numbers and Bernoulli polynomials [PDF]
Discrete Applied Mathematics, 2000 Let \(B_n(x)\), resp. \(B_n\), denote the classical Bernoulli polynomial, resp. number. In the paper under review the author proves some generalizations of Kummer's congruence by determining \[ \frac{B_{k(p-1)+b}(x)}{(k(p-1)+b)}\pmod{p^n} \] where \(p\) is an odd prime, \(x\) a \(p\)-integral rational number and \(p-1\nmid b\), while Kummer considered ...
Zhi-Hong Sun, Sun, Zhi-Hong
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ON RECURRENCE RELATIONS FOR BERNOULLI POLYNOMIALS AND NUMBERS [PDF]
Facta Universitatis, Series: Mathematics and InformaticsIn this work we connect Bernoulli numbers and polynomials to Mersenne numbers via recurrence relations. We find two explicit formulas of Bernoulli numbers by means of Mersenne numbers different from those given by F. Qi and X. Y. Chen et al. To end with other interesting relationships, which serve as bridges between the Bernoulli polynomials and ...
Goubi, Mouloud
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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 ...
Qi, Feng, Luo, Qiu-Ming
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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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Inequalities of Some Trigonometric Functions [PDF]
, 2003 By using two identities and two inequalities relating to Bernoulli’s and Euler’s numbers and power series expansions of cotangent function, secant function, cosecant function and logarithms of functions involving sine function, cosine function and ...
Qi, Feng, Chen, Chao-Ping
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Advances in Difference Equations, 2011 This paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials given by Acikgöz et al. (Adv Differ Equ, Article ID 951764, 9, 2010), some incorrect properties are revised.
Kim Taekyun, Lee Byungje, Ryoo Cheon
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