Related papers: On Generalized Multi Poly-Euler and Multi Poly-Ber…
In this paper, we investigated properties of Tribonacci-Lucas polynomials which generalized Tribonacci-Lucas numbers. From this generalization, we also obtain some new algebraic properties on these numbers and polynomials as Binet formula,…
In this note, we obtain some identities for the generalized Fibonacci polynomial by using the Q(x) matrix. These identities including the Cassini identity and Honsberger formula can be applied to some polynomial sequences, such as Fibonacci…
In this paper, we give some new and interesting identities which are derived from the basis of Frobenius-Euler. Recently, Simsek et als(see [13]) have given some identities of q-analogue of Frobenius-Euler polynomials related to q-Bernstein…
We define \emph{generalized standard triples} $\mathbf{X}$, $\mathbf{Y}$, and $L(z) = z\mathbf{C}_{1} - \mathbf{C}_{0}$, where $L(z)$ is a linearization of a regular matrix polynomial $\mathbf{P}(z) \in \mathbb{C}^{n \times n}[z]$, in order…
We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.
In this paper we establish two symmetric identities on sums of products of Euler polynomials.
By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the…
In this work we propose a combinatorial model that generalizes the standard definition of permutation. Our model generalizes the degenerate Eulerian polynomials and numbers of Carlitz from 1979 and provides missing combinatorial proofs for…
As properties of poly-Bernoulli numbers, a number of formulas such as the duality formula, explicit formula using the Stirling numbers of the second kind and periodicity for negative upper-index have been established. For the multi-indexed…
Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums), which, within the past decade, have arisen in…
In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
For finite sums of non-negative powers of arithmetic progressions the generating functions (ordinary and exponential ones) for given powers are computed. This leads to a two parameter generalization of Stirling and Eulerian numbers. A…
The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…
In this paper, we study some symmetric properties of the multiple q-Euler zeta function. From these properties, we derive several identities of symmetry for the (h;q)-extension of higher-order Euler polynomials.
We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using…
This paper introduces a degenerate version of the Euler-Seidel method by incorporating a parameter lambda into the classical recurrence relation. We define a degenerate Euler-Seidel matrix associated with an initial sequence and establish…
In this paper, we provide a probabilistic interpretation of the Volkenborn integral; this allows us to extend results by T. Kim et al about sums of Euler numbers to sums of Bernoulli numbers. We also obtain a probabilistic representation of…
The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include…
In this paper, we introduce the hypergeometric Euler number as an analogue of the hypergeometric Bernoulli number and the hypergeometric Cauchy number. We study several expressions and sums of products of hypergeometric Euler numbers. We…