In this work, we study the asymptotic properties of a new Sturm-Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered ...

In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by n(a, B) and n(a, E), respectively. Secondly, we derive the mean value of a ...

In the paper, we define Laguerre-based Hermite-Bernoulli polynomial with its generating function, and investigate certain properties. From this generating function, we derive summation formulas and related bilateral series ...

Motivated by Kurt's blending generating functions of q-Apostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized ...

In this note, we present Kantorovich modification of the operators introduced by V. Mihesan [Creative Math. Inf. 17 (2008), 466 - 472]. First, we derive some indispensable auxiliary results in the second section. We present ...

In this paper, we introduce a new generalization of the Hermite polynomials via (p,q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, ...

We introduce Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-invairant integral in the p-adic integer ring and obtain some new interesting identities. Using a complex contour integral representation ...

The main purpose of this paper is to introduce (p, q)-Frobenius-Euler numbers and polynomials, and to investigate their some identities and properties including addition property, difference equation, derivative property, ...

In the paper, we introduce an analogue of Haar distribution based on (rho, q)-numbers, as follows: mu(rho,q) (a + p(N)Z(p)) = rho(pN)/[p(N)](rho,q) (q/rho)(a) By means of this distribution, we derive (rho, q)-analogue ...

In the present paper, we introduce a method in order to obtain some new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived from Bernoulli polynomial basis. Finally, ...