Results 61 to 70 of about 10,388 (168)
Some Identities on Bernoulli and Euler Numbers
Discrete Dynamics in Nature and Society, 2012 Recently, Kim introduced the fermionic p-adic integral on Zp. By using the equations of the fermionic and bosonic p-adic integral on Zp, we give some interesting identities on Bernoulli and Euler numbers.
D. S. Kim, T. Kim, J. Choi, Y. H. Kim
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Applications of a Recurrence for the Bernoulli Numbers
Journal of Number Theory, 1995 The author provides an easy proof of the recurrence \[ B_m= {1\over {n(1- n^m)}} \sum^{m-1}_{k =0} n^k {m \choose k} B_k \sum^{n-1}_{j=1} j^{m-k}, \] where \(\{B_m\}\) are the Bernoulli numbers. The author uses this formula to present proofs of theorems on Bernoulli numbers due to Staudt-Clausen, Carlitz, Frobenius and Ramanujan.
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Arithmetic Identities Involving Bernoulli and Euler Numbers
International Journal of Mathematics and Mathematical Sciences, 2012 The purpose of this paper is to give some arithmatic identities for the Bernoulli and Euler numbers. These identities are derived from the several p-adic integral equations on ℤp.
H.-M. Kim, D. S. Kim
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A new construction on the
Advances in Difference Equations, 2011 This paper performs a further investigation on the q-Bernoulli polynomials and numbers given by Açikgöz et al. (Adv. Differ. Equ. 2010, 9, Article ID 951764) some incorrect properties are revised.
Bayad Abdelmejid +4 more
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On Carlitz's q-Bernoulli numbers
Journal of Number Theory, 1982 Bernoulli numbers and polynomials can be used to define \(p\)-adic analogues of the classical zeta function and \(L\)-functions (as an integral of a simple function with respect to a measure that is a regularization of a Bernoulli distribution, see [the author, \(p\)-adic numbers, \(p\)-adic analysis, and zeta-functions.
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A new class of generalized polynomials associated with Hermite and Bernoulli polynomials
Le Matematiche, 2015 In this paper, we introduce a new class of generalized polynomials associated with the modified Milne-Thomson's polynomials Φ_{n}^{(α)}(x,ν) of degree n and order α introduced by Derre and Simsek.The concepts of Bernoulli numbers B_n, Bernoulli ...
M. A. Pathan, Waseem A. Khan
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A New Approach to
Advances in Difference Equations, 2010 We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials.
Açikgöz Mehmet +2 more
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On p-Bernoulli numbers and polynomials
Journal of Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hankel determinants and Jacobi continued fractions for $q$-Euler numbers
Comptes Rendus. MathématiqueThe $q$-analogs of Bernoulli and Euler numbers were introduced by Carlitz in 1948. Similar to recent results on the Hankel determinants for the $q$-Bernoulli numbers established by Chapoton and Zeng, we perform a parallel analysis for the $q$-Euler ...
Chern, Shane, Jiu, Lin
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