相关论文: New identities involving Bernoulli and Euler polyn…

In this paper we prove a family of identities for Bernoulli numbers parameterized by triples of integers $(a,b,c)$ with $a+b+c=n-1$, $n\ge 4$. These identities are deduced while translating into homotopical terms the gauge action on the…

We offer several new summation identities involving harmonic numbers, odd harmonic numbers, and Fibonacci numbers. Our results are derived using three different approaches: partial summation, polynomial identities and binomial…

In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic…

We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.

In this paper, we define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi…

We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials. We consider some applications of…

In this paper, we consider Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of these polynomials arising from umbrral calculus, we derive new and interesting identities.

We review and discuss some results on the representation of Bernoulli, poly-Bernoulli numbers, and Bernoulli and Cauchy polynomials in terms of Stirling numbers of the first or second kind, or in terms of r-Stirling numbers.

It is known that Bernoulli scheme of independent trials with two outcomes is connected with the binomial coefficients. The aim of this paper is to indicate stochastic processes which are connected with the $q$-polynomial coefficients (in…

A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.

In a recent paper, Yu. A. Brychkov derived a series of identities for multiples sums of special functions, using generating functions. Among these identities, a particularly interesting one involves multiples sums of Bessel $I_{\nu}$…

In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.

In the paper, the author elementarily unifies and generalizes eight identities involving the functions $\frac{\pm1}{e^{\pm t}-1}$ and their derivatives. By one of these identities, the author establishes two explicit formulae for computing…

We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

The object of this paper is to introduce and study properties of unified Apostol-Bernoulli and Apostol-Euler polynomials noted by $\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n \geq 0}$. We study some arithmetic properties of…

We derive two new generalizations of the Busche-Ramanujan identities involving the multiple Dirichlet convolution of arithmetic functions of several variables. The proofs use formal multiple Dirichlet series and properties of symmetric…

In the present paper, we deal mainly with arithmetic properties of Legendre polynomials by using their orthogonality property. We show that Legendre polynomials are proportional with Bernoulli, Euler, Hermite and Bernstein polynomials.

Identities between Whittaker and modified Bessel functions are derived for particular complex orders. Certain polynomials appear in such identities, which satisfy a fourth order differential equation (not of hypergeometric type), and they…