Related papers: A Note on the generating function of p-Bernoulli n…
In this work we derive a bilateral generating function involving the product of an Appell-type product of the Bernoulli and Euler polynomials over independent indices and orders. This function is expressed in terms of the Hurwitz zeta…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this…
We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings…
We compute the generating function of column-strict plane partitions with parts in {1,2,...,n}, at most c columns, p rows of odd length and k parts equal to n. This refines both, Krattenthaler's ["The major counting of nonintersecting…
The results in the preceding comment are placed on a more general mathematical foundation.
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
This paper has more formal series with Bernoulli numbers and the Riemann zeta function. He gives the generating function for the Bernoulli numbers. The paper is translated from the Latin original into German.
For two natural numbers $1<p_1<p_2$, with $\alpha = \frac{\log(p_1)}{\log(p_2)}$ irrational, we describe, in main Theorem $\Omega$ and in Note $1.5$, the factorization of two adjacent numbers in the multiplicatively closed subset $S =…
In this paper we give some interesting equation of p-adic q-integrals on Zp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli numbers and polynomials in p-adic number field.
In the paper, by establishing a new and explicit formula for computing the $n$-th derivative of the reciprocal of the logarithmic function, the author presents new and explicit formulas for calculating Bernoulli numbers of the second kind…
A generating function of the number of homomorphisms from the fundamental group of a compact oriented or non-orientable surface without boundary into a finite group is obtained in terms of an integral over a real group algebra. We calculate…
This is the first of two articles devoted to a comprehensive exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker coefficients. We also…
We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the…
Given a sequence of independent Bernoulli variables with unknown parameter $p$, and a function $f$ expressed as a power series with non-negative coefficients that sum to at most $1$, an algorithm is presented that produces a Bernoulli…
In this note, we shall obtain two closed forms for the Apostol-Bernoulli polynomials.