AbstractEuler's well-known nonlinear relation for Bernoulli numbers, which can be written in symbolic notation as (B0+B0)n=−nBn−1−(n−1)Bn, is extended to (Bk1+⋯+Bkm)n for m⩾2 and arbitrary fixed integers k1,…,km⩾0. In the general case we prove an existence theorem for Euler-type formulas, and for m=3 we obtain explicit expressions. This extends the authors' previous work for m=2
AbstractIn this paper, we obtain a simple property of the Bernoulli polynomials Bn(x) and the Euler ...
AbstractWe define higher or arbitrary order universal Bernoulli numbers and higher order universal B...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractWe extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can ...
AbstractEuler's well-known nonlinear relation for Bernoulli numbers, which can be written in symboli...
AbstractIn this paper, by the generating function method, we establish various identities concerning...
AbstractThe purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli n...
We give an elementary proof of a generalization of the Seidel-Kaneko and Chen-Sun formula involving...
We prove several explicit formulae for the $n$-th Bernoulli polynomial $B_{n}(x)$, in which $B_{n}(x...
We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in ...
We present a proof of an identity involving the Bernoulli numbers. This identity has been proved, ov...
AbstractClosed expressions are obtained for sums of products of Bernoulli numbers of the form[formul...
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The g...
AbstractIn this paper, our aim is to investigate the summation form of Bernoulli numbers Bn, such as...
AbstractWe employ the basic properties for the Hasse–Teichmüller derivatives to give simple proofs o...
AbstractIn this paper, we obtain a simple property of the Bernoulli polynomials Bn(x) and the Euler ...
AbstractWe define higher or arbitrary order universal Bernoulli numbers and higher order universal B...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
AbstractWe extend Euler's well-known quadratic recurrence relation for Bernoulli numbers, which can ...
AbstractEuler's well-known nonlinear relation for Bernoulli numbers, which can be written in symboli...
AbstractIn this paper, by the generating function method, we establish various identities concerning...
AbstractThe purpose of this paper is to give a proof of Kummer type congruence for the q-Bernoulli n...
We give an elementary proof of a generalization of the Seidel-Kaneko and Chen-Sun formula involving...
We prove several explicit formulae for the $n$-th Bernoulli polynomial $B_{n}(x)$, in which $B_{n}(x...
We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in ...
We present a proof of an identity involving the Bernoulli numbers. This identity has been proved, ov...
AbstractClosed expressions are obtained for sums of products of Bernoulli numbers of the form[formul...
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The g...
AbstractIn this paper, our aim is to investigate the summation form of Bernoulli numbers Bn, such as...
AbstractWe employ the basic properties for the Hasse–Teichmüller derivatives to give simple proofs o...
AbstractIn this paper, we obtain a simple property of the Bernoulli polynomials Bn(x) and the Euler ...
AbstractWe define higher or arbitrary order universal Bernoulli numbers and higher order universal B...
AbstractWe give a p-adic proof of a certain new relation between the Bernoulli numbers Bk, similar t...
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