In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the ...

In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Lucas numbers and Fibonacci polynomials. By making use of the new operator defined in this paper, we give ...

In this paper, we derive some new symmetric properties of k-Fibonacci numbers by making use of symmetrizing operator. We also give some new generating functions for the products of some special numbers such as k-Fibonacci ...

In this paper, we develop the theory of the multiple q-analogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple q-antiderivative and ...

In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral ...

In the present paper, we find the Fourier expansion of the Apostol Frobenius-Euler polynomials. By using a Fourier expansion of the Apostol Frobenius-Euler polynomials, we derive some new and interesting results.

In the paper, using the extended fermionic p-adic integral on Z(p), the authors find some applications of the umbral calculus. From these applications, the authors derive some identities on the weighted Euler numbers and ...

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 ...