Related papers: Construction a new generating function of Bernstei…
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…
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…
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…
Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…
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…
The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extensions of Hurwitz-zeta type functions from the…
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
The main objective of this paper is to introduce the modified q-Genocchi polynomials and to define their generating function. In the paper, we show new relations, which are explicit formula, derivative formula, multiplication formula, and…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
In this paper, we introduce a new class of polynomials, called probabilistic q-Bernstein polynomials, alongside their generating function. Assuming Y is a random variable satisfying moment conditions, we use the generating function of these…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…
The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…
The first aim of this paper is to construct new generating functions for the generalized {\lambda}-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers, attached…
In this paper, using geometric polynomials, we obtain a generating function of p-Bernoulli numbers. As a consequences this generating function, we derive closed formulas for the finite summation of Bernoulli and harmonic numbers involving…
The aim of this paper is to construct general forms of ordinary generating functions for special numbers and polynomials involving Fibonacci type numbers and polynomials, Lucas numbers and polynomials, Chebyshev polynomials, Sextet…
By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions…
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating…
One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…
In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying…