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Full-Text Articles in Physical Sciences and Mathematics
Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m
Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m
Turkish Journal of Mathematics
According to the generalized Mellin derivative, we introduce a new family of polynomials called higher order generalized geometric polynomials and obtain some arithmetical properties of them. Then we investigate the relationship of these polynomials with degenerate Bernoulli, degenerate Euler, and Bernoulli polynomials. Finally, we evaluate several series and integrals in closed forms.
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Some Series Involving The Euler Zeta Function, Min-Soo Kim
Turkish Journal of Mathematics
In this paper, using the Boole summation formula, we obtain a new integral representation of $n$-th quasi-periodic Euler functions $\overline{E}_n(x)$ for $n=1,2,\ldots.$ We also prove several series involving Euler zeta functions $\zeta_{E}(s),$ which are analogues of the corresponding results by Apostol on some series involving the Riemann zeta function $\zeta(s).$
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
Turkish Journal of Mathematics
Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed …