Related papers: A curious identity for Bernoulli numbers
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
In this note we present a combinatorial proof of an identity involving poly-Bernoulli numbers and Genocchi numbers. We introduce the combinatorial objects, $m-$barred Callan sequences and show that the identity holds in a more general…
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.
We generalise the Bernoulli numbers to include the case where the index may be a continuous variable.
In this paper, we give the determinant expressions of the hypergeometric Bernoulli numbers, and some relations between the hypergeometric and the classical Bernoulli numbers which include Kummer's congruences. By applying Trudi's formula,…
Given an odd prime p, we present three independent ways of relating modulo p certain truncated convolutions of divided Bernoulli numbers to certain full convolutions of divided Bernoulli numbers.
We establish a new identity linking Bernoulli, Stirling (first kind), and Bessel (first kind) numbers: \[ \sum_{k=0}^{n} 2^{\,n-k}\,s(n,k)\,B_k \;=\; \sum_{k=0}^{n} b(n,k)\,\frac{(-1)^k\,k!}{k+1}. \] This parallels the classical…
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
The purpose of this paper is to derive some identities of the higher order generalized twisted Bernoulli numbers and polynomials attached to $\chi$ from the properties of the p-adic invariant integrals.
In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas…
In 2002 Zhi-Wei Sun [Integers 2(2002)] published a curious identity involving binomial coefficients. In this paper we present a generalization of the identity.
The distribution of the spectral numbers of an isolated hypersurface singularity is studied in terms of the Bernoulli moments. These are certain rational linear combinations of the higher moments of the spectral numbers. They are related to…
We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.
We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes. We also discuss some applications and related open problems.
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…
In this note we prove combinatorially some new formulas connecting poly-Bernoulli numbers with negative indices to Eulerian numbers.
In this paper, we investigate some properties of q-Bernoulli polynomi- als arising from q-umbral calculus. Finally, we derive some interesting identities of q-Bernoulli polynomials from our investigation.
Based on an interesting identity of Bat{\i}r we derive new identities for double sums involving famous number sequences. We also prove some double sum identities for binomial transform pairs.
Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…
We introduce generalized hypergeometric Bernoulli numbers for Dirichlet characters. We study their properties, including relations, expressions and determinants. At the end in Appendix we derive first few expressions of these numbers.