7 papers
Harmonic numbers and Lerch functions behind falling factorial generating functions
Hemen Dutta, Gradimir V. Milovanovic, Yilmaz Simsek
We study a family of special numbers and polynomials introduced by Simsek whose exponential generating function has as denominator a falling factorial in the exponential variable.…
Exponential generating functions for Apostol-Dedekind and related sums
Yilmaz Simsek
One of the primary objectives of this paper is to construct generating functions for Apostol-Dedekind sums. These exponential generating functions greatly facilitate the discovery…
Certain families of series involving Hurwitz and Lerch zeta functions
Dora Pokaz, Mihaela Ribicic Penava, Yilmaz Simsek
This paper deals with a certain family of series which is derived from generating functions of the Frobenius-Euler and Apostol type polynomials and numbers. When special cases of t…
Novel computational formulas and relations for special numbers and functions: approach to analysis of Debye functions
Yilmaz Simsek
The first goal of this paper is to give a new family of special function related to the Debye functions. By using these function and generating function method, we derive many nove…
Novel series involving families of zeta functions and special functions and polynomials by applying Norlund sum and derivative formula
Elif Sukruoglu, Yilmaz Simsek
In recent years, the Norlund sum and its applications have attracted considerable attention, especially in mathematics and other applied sciences. Because this sum plays an importa…
Fourier representations of fractional B Splines via generalized Stirling type polynomials
Damla Gun, Peter Massopust, Yilmaz Simsek
In this paper, we investigate fractional B splines and their connections with Fourier analysis, and establish connections with generalized Stirling-type numbers and distribution th…
Formulas of special polynomials involving Bernoulli polynomials derived from matrix equations and Laplace transform
Ezgi Polat, Yilmaz Simsek
The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformati…