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IDENTITIES AND RELATIONS RELATED TO COMBINATORIAL NUMBERS AND POLYNOMIALS
Yilmaz Simsek 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.1
This paper presents some new families of special numbers and polynomials including the Euler numbers and polynomials, the Stir- ling numbers of the second kind, the central factorial numbers and the array polynomials. We give some properties of these numbers and poly- nomials with their generating functions. Finally, by using these generat- ing functions with their functional equations, we derive some identities and relations realeted to these special numbers and polynomials.
ON ELLIPTIC ANALOGUE OF THE HARDY SUMS
Simsek, Yilmaz,Kim, Dae-Yeoul,Koo, Ja-Kyung Korean Mathematical Society 2009 대한수학회보 Vol.46 No.1
Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.
ON q-ANALGUE OF THE TWISTED L-FUNCTIONS AND q-TWISTED BERNOULLI NUMBERS
Simsek, Yilmaz Korean Mathematical Society 2003 대한수학회지 Vol.40 No.6
The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\;X,\;{\xi})$ is also given explicitly.
On elliptic analogue of the Hardy sums
Yilmaz Simsek,Daeyeoul Kim,구자경 대한수학회 2009 대한수학회보 Vol.46 No.1
Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given. Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.
INTERPOLATION FUNCTIONS OF THE EULERIAN TYPE POLYNOMIALS AND NUMBERS
Yilmaz Simsek 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
The purpose of this paper is to give the family of interpolation functions of the Eulerian type polynomials and numbers. We derive some identities related to not only these functions, but also these polynomials and numbers.
p-ADIC q-HIGHER-ORDER HARDY-TYPE SUMS
SIMSEK YILMAZ Korean Mathematical Society 2006 대한수학회지 Vol.43 No.1
The goal of this paper is to define p-adic Hardy sums and p-adic q-higher-order Hardy-type sums. By using these sums and p-adic q-higher-order Dedekind sums, we construct p-adic continuous functions for an odd prime. These functions contain padic q-analogue of higher-order Hardy-type sums. By using an invariant p-adic q-integral on $\mathbb{Z}_p$, we give fundamental properties of these sums. We also establish relations between p-adic Hardy sums, Bernoulli functions, trigonometric functions and Lambert series.
ON TWISTED GENERALIZED EULER NUMBERS
Simsek, Yilmaz Korean Mathematical Society 2004 대한수학회보 Vol.41 No.2
In this paper, we shall construct generating function of twisted generalized Euler numbers. By using this function, we shall define twisted generalized Euler polynomials and numbers. We shall give some basic properties of these polynomials and numbers.
On $q$-analgue of the twisted $L$-functions and\ $q$-twisted Bernoulli\ numbers
Yilmaz Simsek 대한수학회 2003 대한수학회지 Vol.40 No.6
The aim of this work is to construct twisted $q$-$L$-series which interpolate twisted $q$-generalized Bernoulli numbers. By using generating function of $q$-Bernoulli numbers, twisted $q$-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers $L_{q}(1-n,\chi,\xi)$ is also given explicitly.
On twisted generalized Euler numbers
Yilmaz Simsek 대한수학회 2004 대한수학회보 Vol.41 No.2
In this paper, we shall construct generating function of twistedgeneralized Euler numbers. By using this function, we shall definetwisted generalized Euler polynomials and numbers. We shall givesome basic properties of these polynomials and numbers.