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GENERALIZATION OF q-APOSTOL-TYPE EULERIAN NUMBERS AND POLYNOMIALS, AND THEIR INTERPOLATION FUNCTIONS
I. N. Cangul,A. S. Cevik,Y. Simsek 장전수학회 2015 Advanced Studies in Contemporary Mathematics Vol.25 No.2
In a recent paper [16], generating functions in terms of non- negative real parameters, q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius-Euler numbers and polynomials) have been constructed by Y. Simsek. Additionally, some identities for these poly- nomials and numbers based on the generating functions and functional equations have been derived. Finally, a multiplication formula for the generalized Apostol type Frobenius-Euler polynomials has been given. In this paper, as a continuing study of [16], we will essentially present generalizations of the above material and, dierently from aforemen- tioned paper, we will express the interpolation functions related to these numbers and polynomials.
On interpolation functions of the twisted generalized Frobenius-Euler numbers
Y. Simsek,V. Kurt,O. Yurekli 장전수학회 2007 Advanced Studies in Contemporary Mathematics Vol.15 No.2
The main purpose of this paper is to apply Mellin transform to the generating functions of q-generalized Frobenius-Euler numbers and twisted q-generalized Frobenius-Euler numbers. By using this result, we define integral representation of twisted lH;q-function, which interpolates twisted q-generalized Frobenius- Euler numbers at negative integers. We also define twisted q-zeta functions. Furthermore, we give relation between twisted lH;q-functions and twisted q-zeta functions. We obtain new results related to the twisted lH;q-function, as well.
Applications of umbral algebra to some special polynomials
R. Dere,Y. Simsek 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.3
In this work, we study on umbral algebra and generating functions for the Hermite type Genocchi polynomials and numbers. We introduce some properties of this algebra and polynomials.
A note on p -adic q -Euler measure
H. Ozden,Y. Simsek,S.-H. Rim,I. Cang?l 장전수학회 2007 Advanced Studies in Contemporary Mathematics Vol.14 No.2
In this paper, we wil investigate some interesting properties of the modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measureon Zp.
ON THE HIGHER-ORDER w-q-GENOCCHI NUMBERS
I. N.. Cangul,H. Ozden,V. Kurt,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
Main purpose of this paper is to study on higher-order w-q-Genocchi numbers and polynomials by using p-adic q-deformed fermi- onic integral on Zp. We derive some identities related to higher-order w-q- Genocchi numbers and polynomials. We also give interpolation functions of these numbers and polynomials.
Remarks on q-Bernoulli numbers associated with Daehee numbers
H. Ozden,I. N. Cangul,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
In this work, we study on Carlitz's type q-Bernoulli numbers, q-Frobenius-Euler numbers and Daehee numbers and polynomials. We also give p-adic integral representation of the twisted Daehee polynomials. By using this representation, we ¯nd Raabe-type multiplication formula for the twisted Daehee polynomials.
A note on the alternating sums of powers of consecutive q-integers
T. Kim,S.-H. Rim,Y. Simsek 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.2
In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.
Twisted Dedekind type sums associated with Barnes' type multiple Frobenius-Euler l-functions
M. Can,M. Cenkci,V. Kurt,Y. Simsek 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.2
The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes' type multiple Frobenius-Euler numbers and polynomials. By applying Mellin transformation to these functions, we de¯ne Barnes' type multiple l-functions, which interpolate Frobenius-Euler numbers at negative integers. By using generalizations of the Frobenius-Euler functions, we de¯ne generalized Dedekind type sums and prove corresponding reciprocity law. We also give twisted versions of the Frobenius-Euler polynomials and new Dedekind type sums and corresponding reciprocity law. Furthermore, by using p-adic q-Volkenborn integral and twisted (h,q)-Bernoulli functions, we construct p-adic (h,q)-higher order Dedekind type sums. By using relation between Bernoulli and Frobenius-Euler functions, we also de¯ne analogues of Hardy-Berndt type sums. We give some new relations related to to these sums as well.