Results 11 to 20 of about 703 (65)
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 12, Page 599-605, 2004., 2004 We consider the modified q‐analogue of Riemann zeta function which is defined by ζq(s)=∑n=1∞(qn(s−1)/[n]s), 0 < q < 1, s ∈ ℂ. In this paper, we give q‐Bernoulli numbers which can be viewed as interpolation of the above q‐analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at ...
Taekyun Kim
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An extension of q‐zeta function
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 49, Page 2649-2651, 2004., 2004 We will define the extension of q‐Hurwitz zeta function due to Kim and Rim (2000) and study its properties. Finally, we lead to a useful new integral representation for the q‐zeta function.
T. Kim, L. C. Jang, S. H. Rim
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Polynomial extension of Fleck's congruence [PDF]
, 2005 Let $p$ be a prime, and let $f(x)$ be an integer-valued polynomial. By a combinatorial approach, we obtain a nontrivial lower bound of the $p$-adic order of the sum $$\sum_{k=r(mod p^{\beta})}\binom{n}{k}(-1)^k f([(k-r)/p^{\alpha}]),$$ where $\alpha\ge ...
Sun, Zhi-Wei
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Generalizations of Bernoulli numbers and polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 59, Page 3769-3776, 2003., 2003 The concepts of Bernoulli numbers Bn, Bernoulli polynomials Bn(x), and the generalized Bernoulli numbers Bn(a, b) are generalized to the one Bn(x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between Bn, Bn(x), Bn(a, b), and Bn(
Qiu-Ming Luo +3 more
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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Explicit Formulas involving q-Euler Numbers and Polynomials [PDF]
, 2012 In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator.
Acikgoz, Mehmet +2 more
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Generalizations of Euler numbers and polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 61, Page 3893-3901, 2003., 2003 The concepts of Euler numbers and Euler polynomials are generalized and some basic properties are investigated.
Qiu-Ming Luo, Feng Qi, Lokenath Debnath
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Two closed forms for the Bernoulli polynomials [PDF]
, 2015 In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.Comment: 7 ...
Chapman, Robin J., Qi, Feng
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On equal values of power sums of arithmetic progressions [PDF]
, 2012 In this paper we consider the Diophantine equation \begin{align*}b^k +\left(a+b\right)^k &+ \cdots + \left(a\left(x-1\right) + b\right)^k=\\ &=d^l + \left(c+d\right)^l + \cdots + \left(c\left(y-1\right) + d\right)^l, \end{align*} where $a,b,c,d,k,l$ are ...
Bazsó, A. +3 more
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Construction a new generating function of Bernstein type polynomials
, 2010 Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given.
Simsek, Yilmaz
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