Related papers: Schur type poly-Bernoulli numbers
We introduce and study a `level two' generalization of the poly-Bernoulli numbers, which may also be regarded as a generalization of the cosecant numbers. We prove a recurrence relation, two exact formulas, and a duality relation for…
The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood from the multiplication in the space of…
Jacobi-Trudy formula for a generalisation of Schur polynomials related to any sequence of orthogonal polynomials in one variable is given. As a corollary we have Giambelli formula for generalised Schur polynomials.
Recently, Komatsu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we consider the new concept of higher-order Cauchy numbers and polynomials which generalize…
We define a generalized class of modified zeta series transformations generating the partial sums of the Hurwitz zeta function and series expansions of the Lerch transcendent function. The new transformation coefficients we define within…
In this paper we announce some results obtained for certain algebraic functions, which we call of cyclotomic type. The main results properly resemble von Staudt-Clausen's theorem and Kummer's congruence for the Bernoulli numbers, and such…
We prove several Stern's type congruences for generalized bernoulli numbers.
Let $p,x$ be real numbers, and $s$ be a complex number, with $\Re(s)>1-r$, $p\geq 1$, and $x+1>0$. The zeta function $Z^{\bf\alpha}_p(s;x)$ is defined by $$ Z^{\bf\alpha}_p(s;x) =\frac{1}{\Gamma(s)}\int^\infty_0 \frac{e^{-xt}}…
This paper shows that a finite discrete convolution involving Stirling numbers of both kinds and harmonic numbers can be expressed in terms of the Bernoulli numbers. As applications of this expression, the linear recurrence relation for the…
Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previously known results. These formulas provide a well-defined algorithm for computing Selberg-Schur…
The Brenke type generating functions are the polynomial generating functions of the form $$\sum_{n=0}^{\infty}{P_n(x )\over n!}t^n=A(t)B(xt), $$ where $A$ and $B$ are two formal power series subject to the conditions…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
A generalization of a well-known relation between the Riemann zeta function $\zeta(s)$ and Bernoulli numbers $B_n$ is obtained. The formula is a new representation of the Riemann zeta function in terms of a nested series of Bernoulli…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
We establish supercongruences for two kinds of Ap\'ery-like numbers, which involve Bernoulli numbers and Bernoulli polynomials. Conjectural supercongruences of the same type for another four kinds of Ap\'ery-like numbers are also proposed.
Alternating variants of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p This paper consists of two parts: the characteristic 0 part and the characteristic p part. In characteristic 0 part, we…
The main objective of this paper is to present recurrence relations for the generalized poly-Cauchy numbers and polynomials. This is accomplished by introducing the concept of generalized m-poly-Cauchy numbers and polynomials. Additionally,…
The main object of this paper is to construct a new generating function of the (q-) Bernstein type polynomials. We establish elementary properties of this function. By using this generating function, we derive recurrence relation and…