Serkan Araci

Serkan Araci
Hasan Kalyoncu University · Department of Economics

PhD

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265
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Publications

Publications (265)
Article
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The logarithmic functions have been used in a verity of areas of mathematics and other sciences. As far as we know, no one has used the coefficients of logarithmic functions to determine the bounds for the third Hankel determinant. In our present investigation, we first study some well-known classes of starlike functions and then determine the thir...
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In this paper, the theory of symmetric q-calculus and conic regions are used to define a new subclass of q-starlike functions involving a certain conic domain. By means of this newly defined domain, a new subclass of normalized analytic functions in the open unit disk E is given. Certain properties of this subclass, such as its structural formula,...
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The fundamental aim of this paper is to derive the recurrence relation, shift operators, differential, integrodifferential and partial differential equations for Gould–Hopper–Frobenius–Euler polynomials using factorization method, which may be utilised in solving some emerging problems in different branches of science and technology.
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In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new subclass of analytic and bi-univalent functions. F...
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A variety of functions, their extensions, and variants have been extensively investigated, mainly due to their potential applications in diverse research areas. In this paper, we aim to introduce a new extension of Whittaker function in terms of multi-index confluent hypergeometric function of first kind. We discuss multifarious properties of newly...
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In recent years, special functions such as Bessel functions have been widely used in many areas of mathematics and physics. We are essentially motivated by the recent development; in our present investigation, we make use of certain conic domains and define a new class of analytic functions associated with the Dini functions. We derive inclusion re...
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Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions...
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To date, many interesting subclasses of analytic functions involving symmetrical points and other well celebrated domains have been investigated and studied. The aim of our present investigation is to make use of certain Janowski functions and a Mathieu-type series to define a new subclass of analytic (or invariant) functions. Our defined function...
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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 numbers, k-Pell numbers, Jacobsthal numbers, Fibonacci polynomials and Chebyshev polynomials.
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This paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various types of q-Bessel functions and some power series of special type. It has been obtained for basic q-generating series, q-exponential and q-...
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In the present investigation, with the help of certain higher-order q -derivatives, some new subclasses of multivalent q -starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient con...
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By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we in...
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In this article, for the incomplete H -functions, we obtain a set of new generating functions. The bilateral along with linear generating relations are derived for the incomplete H -functions. Many of the generating functions readily accessible in the literature are often deemed as implementations of the main findings. All the derived findings are...
Article
A remarkably large number of polynomials and their extensions have been presented and studied. In the present paper, we introduce the new type of generating function of Appell-type Changhee-Euler polynomials by combining the Appell-type Changhee polynomials and Euler polynomials and the numbers corresponding to these polynomials are also investigat...
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In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolution products. Then we prove that the extended Cherednik–Opdam integral operator is linear, bijective and continuous with respect to the conve...
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Our aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize the Gram–Schmidt orthogonalization process to create...
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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 some new generating functions for k-Fibonacci and Pell numbers and Fibonacci polynomials.
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This paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta s...
Article
In this paper, we give some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q) -Lucas numbers, (p, q)-Pell numbers, -Pell Lucas numbers, (p, q)-Jacobsthal numbers, and (p, q)- Jacobsthal Lucas numbers with 2-orthogonal Chebyshev polynomials and trivariate Fibonacci polynomials.
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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 second kind. Then, we introduce Bell-based Bernoulli polynomials of order and investigate multifarious correlations and formulas i...
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In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral ope...
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The present article is aimed at introducing and investigating a new class of q-hybrid special polynomials, namely, q-Fubini-Appell polynomials. The generating functions, series representations, and certain other significant relations and identities of this class are established. Some members of q-Fubini-Appell polynomial family are investigated, an...
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This paper gives an overview of systematic and analytic approach of operational technique involves to study multi-variable special functions significant in both mathematical and applied framework and to introduce new families of special polynomials. Motivation of this paper is to construct a new class of generalized Fubini-type polynomials of the p...
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In the paper, we derive a general case for four weakly compatible self maps satisfying a general contractive condition due to the same method introduced by Altun et al. [2]. We make use of such a study to prove common fixed point theorems for weakly compatible maps along with E.A. and (CLR) properties.
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The devotion of this paper is to study the Bessel function of two variables in k-calculus. we discuss the generating function of k-Bessel function in two variables and develop its relations. After this we introduce the generalized (s, k)-Bessel function of two variables which help to develop its generating function. The s-analogy of k-Bessel functi...
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This work is motivated essentially by the success of the applications of the nonsingular Yang–Abdel–Aty–Cattani (YAC) derivative in many research area of science, engineering, and financial mathematics. Furthermore, the major determination of this survey work is to achieve Fourier transform of the aforesaid new operator. Obviously, the Cauchy‐react...
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In this paper, we employ an umbral method to reformulate the 3-variable Hermite polynomials and introduce the 4-parameter 3-variable Hermite polynomials. We also obtain some new properties for these polynomials. Moreover, some special cases are discussed and some concluding remarks are also given.
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Abstract Kim et al. (Proc. Jangjeon Math. Soc. 21(4):589–598, 2018) have studied the central Fubini polynomials associated with central factorial numbers of the second kind. Motivated by their work, we introduce degenerate version of the central Fubini polynomials. We show that these polynomials can be represented by the fermionic p-adic integral o...
Preprint
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Recently, Kim-Kim [13] have introduced polyexponential functions as an inverse to the polylogarithm functions, and constructed type 2 poly-Bernoulli polynomials. They have also introduced unipoly functions attached to each suitable arithmetic function as a universal concept. Inspired by their work, in this paper, we introduce a new class of the Fro...
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In this paper, the basic analogue of the Laplace transforms involving the product of a general class of q-polynomials along with q-analogue of Fox's H-function and q-analogue of I-function is evaluated. Limiting cases of the main outcomes are also evaluated. The paper shows a large variety of outcomes that can be achieved.
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The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright function, expressed in terms of generalized Wright hypergeometric function and also in terms of generalized hypergeometric function. Based on the main results, some integral formulas involving different special functions that show a c...
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In this paper, we define a new extension of Srivastava’s triple hypergeometric functions by using a new extension of Pochhammer’s symbol that was recently proposed by Srivastava, Rahman and Nisar [H. M. Srivastava, G. Rahman and K. S. Nisar, Some extensions of the Pochhammer symbol and the associated hypergeometric functions, Iran. J. Sci. Technol....
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In this paper, our aim is to finding the solutions of the fractional kinetic equation related with the -Mathieu-type series through the procedure of Sumudu and Laplace transforms. The outcomes of fractional kinetic equations in terms of the Mittag-Leffler function are presented. 1. Introduction and Preliminaries Fractional calculus (FC) can be a v...
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Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227-235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227-235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polyn...
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Kim and Kim (Russ. J. Math. Phys. 26(1):40–49, 2019) have studied the type 2 poly-Bernoulli polynomials. Inspired by their work, we consider a new class of the Frobenius–Genocchi polynomials, which is called the type 2 poly-Frobenius–Genocchi polynomials, by means of the polyexponential function. We also derive some new relations and properties inc...
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Abstract This paper aims to discuss a generalization of certain paraxial diffraction integral operator in a class of generalized functions. At the start of this paper, we propose a convolution formula and establish certain convolution theorem. Then, with the addition to the convolution theorem, we consider a set of approximating identities and subs...
Article
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In this paper, we Örst consider some operators including symmetric functions. From those operators, we obtain some new generating functions of k-Fibonacci numbers and k-Pell numbers of third order and Chebyshev polynomial of the Örst and the second kind.
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In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitl...
Preprint
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In this paper, we consider a class of new generating function for the Frobenius-Genocchi polynomials, called the type 2 degenerate poly-Frobenius-Genocchi polynomials, by means of the polyexponential function. Then, we investigate diverse explicit expressions and some identities for those polynomials.
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We first compute the generating functions by making use of symmetric functions given in this paper. Motivated by the recent works including the products of several special numbers, we are concerned here only with the question of manipulating combinatorial objects, known as symmetric operators. The proposed generalized symmetric functions can be use...
Preprint
The present article aims to introduce a unified family of the Apostol type-truncated exponential-Gould-Hopper polynomials and to characterize its properties via generating functions. A unified presentation of the generating function for the Apostol type-truncated exponential-Gould-Hopper polynomials is established and its applications are given. By...
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Various applications of degenerate polynomials in di¤erent areas call for the thoughtful study and research, and many extensions and variants can be found in the literature. In this paper, we introduce partially degenerate Laguerre-Genocchi polynomials and investigate their properties and identities. Furthermore, we introduce a generalized form of...
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In this paper we propose a new definition of the modified Laplace transform L a (f(t)) for a piece-wise continuous function of exponential order which further reduces to simple Laplace transform for a = e where a = 1 and a > 0. Also we prove some basic results of this modified Laplace transform and connection with different functions.
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The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, series expression, and several explicit and recurrence relations for these polynomials are established. The three-variable general...
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In this article, the general polynomials are taken as base with the Gould-Hopper matrix polynomials to introduce a family of 3-variable general-Gould-Hopper matrix polynomials (3VgGHMaP). These polynomials are framed within the context of monomiality principle and their properties are established. Examples of some members belonging to this family a...
Article
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This paper includes some new investigations and results for post quantum calculus, denoted by (p, q)-calculus. A chain rule for (p, q)-derivative is given. Also, a new (p, q)-analogue of the exponential function is introduced and its properties including the addition property for (p, q)-exponential functions are investigated. Several useful results...
Article
The significance of multi-variable special polynomials has been identified both in mathematical and applied frameworks. The article aims to focus on a new class of 3-variable Legendre-truncated-exponential-based Sheffer sequences and to investigate their properties by means of Riordan array techniques. The quasi-monomiality of these sequences is st...
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In this paper, we establish some new inequalities of Hermite-Hadamard type for the strongly generalized nonconvex function by using the generalized fractional integral operator. Some new results as a special cases are provided as well. At the end, some applications to special mean are obtained.
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In this paper, we first introduce a new family of polynomials, which are called the truncated-exponential based Frobenius-Euler polynomials, based upon an exponential generating function. By making use of this exponential generating function, we obtain their several new properties and explicit summation formulas. Finally, we consider the truncated-...
Article
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In this paper, we introduce a new operator in order to derive some new symmetric properties of Fibonacci numbers and Chebychev polynomials of first and second kind. By making use of the new operator defined in this paper, we give some new generating functions for Fibonacci numbers and Chebychev polynomials of first and second kinds.
Article
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Fractional calculus is allowing integrals and derivatives of any positive order (the term 'fractional' kept only for historical reasons), which can be considered a branch of mathematical physics which mainly deals with integro-differential equations, where integrals are of convolution form with weakly singular kernels of power-law type. In recent d...
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In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived....
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Motivated by Kurt’s blending generating functions of q-Apostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized q-Stirling numbers of the second kind. Additionally, by making use of the fermionic p-adic integral over the p-adic numbers field,...
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In this note, we present Kantorovich modification of the operators introduced by V. Miheşan [Creative Math. Inf. 17 (2008), 466 – 472]. First, we derive some indispensable auxiliary results in the second section. We present a quantitative Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weigh...
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In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Pell numbers and Tchebychev polynomials of first and second kind. By making use of the new operator defined in this paper, we give some new generating functions for k-Fibonacci and k-Pell numbers and Fibonacci polynomials.
Article
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In the paper, we first consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in (p,q)-integers. By making use of these generating functions, we derive (p,q)-generalizations of several old and new identities belonging to Apostol-Bernoulli and Apostol-Euler polynomials. Finally, we define (p,q)-general...
Article
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The article aims to introduce a new unified class of generalized Apostol type polynomials. Further, under a slight modification on the parameters associated to the generalized Apostol type and generalized Gould-Hopper polynomials and by the use of generating method, we introduce a new class of generalized-Apostol-type-Gould-Hopper polynomials. We s...
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Motivated by the construction of the generating functions of q-Bernoulli polynomials and q-Euler polynomials satisfying with their important results, we define a new q-class of the Fubini polynomials. We give some new properties including correlations with the number S_2;q (n; k) given in the paper. We also define two types q-Fubini polynomials wit...
Article
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In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and the familiar Apostol-type polynomials. We also obtain some implicit summation formulas and symmetric identities b...
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Several fractional calculus operators have been introduced and investigated. In this sequence, we aim to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators of extended Mittag-Leffler function (EMLF). We also investigate the statistical distribution associated with the EMLF. F...
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In this paper, we first consider a generalization of Kim's p-adic q-integral on [Formula presented] including parameters α and β. By using this integral, we introduce the q-Daehee polynomials and numbers with weight [Formula presented]. Then, we obtain some interesting relationships and identities for these numbers and polynomials. We also derive s...
Article
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In this paper, the class of q-Sheffer-Appell polynomials is introduced. The generating function, series definition, determinant definition and some other identities of this class are established. Certain members of q-Sheffer-Appell polynomials are investigated and some properties of these members are derived. In addition, the class of 2D q-Sheffer-...
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Let F, N, A and N2 denote the properties of being �nite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of �nitely generated FN-groups. We show that the property FC is closed under �nite extensions, and extend this result to �nitely generated NF-groups. Secondly we prove that a �nitely generated N...
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In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we establish some higher-order convolutions for the Apostol-Bernoulli polynomials, the Apostol-Eul...
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In this article, we introduce new symmetric endomorphism operators by making use of appropriate infinite product series. The main results show that after direct calculations, the proposed operators are qualified to obtain generating functions for k-Jacobsthal numbers and Tchebychev polynomials of the first and second kind.
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We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on Z p. The results presented here, being very general, are shown to reduce to yield symmetr...
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The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several explicit relations involving Hurwitz–Lerch Zeta functions and some summation formulae related to these polynomi...
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In this paper, we introduce a new concept of (ψ - α)-Meir-Keeler- Khan type mappings in partial metric spaces. The presented theorems generalize and improve many existing results in the literature. Moreover, an examples is given to illustrate our results.
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In this paper, we firstly consider the properties of Genocchi polynomials, Fourier series and Zeta functions. In the special cases, we see that the Fourier series yield Zeta functions. From here, we show that zeta functions for some special values can be computed by Genocchi polynomials. Secondly, we consider the Fourier series of periodic Genocchi...
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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 positive logarithm of generating functions of Bernoulli numbers and associated Euler numbers shown as m(2π , B) and m(π , E), respect...
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In the paper, we aim to introduce a new generating function for Laguerre-based Hermite- Bernoulli polynomials and investigate certain properties. From this generating function, we derive summation formulas and related bilateral series associated with the newly introduced generating function. Some of whose special cases are also presented. Relevant...
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We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series. Next, we develop their composition formulas by applying the integral transforms. Finally, we discuss special cases.
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We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations. We also de…ne the Hermite based-Stirling polynomials of the second kind, and then provide some relations. Moreover, we derive several...
Preprint
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This paper includes some new investigations and results for post quantum calculus, denoted by (p,q)-calculus. A chain rule for (p,q)-derivative is developed. Also, a new (p,q)-analogue of the exponential function is introduced and some its properties including the addition property for (p,q)-exponential functions are investigated. Several useful re...
Article
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In this paper, we introduce the generating function of Hermite-based poly-Daehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermite-based poly-Daehee numbers and polynomials including recurrence relations, addition property and correlations with poly-Bernoulli polyn...
Article
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In the paper, we first introduce the fully degenerate Hermite poly-Bernoulli polynomials and investigate their properties. Next, we derive the implicit summation formulae and general symmetry identities by making use of different analytical means and generating function method. The results obtained here are the corresponding generalizations of some...