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Introduction
Special polynomials, Special functions, Umbral calculus, q-calculus, p-adic analysis
Current institution
Additional affiliations
June 2022 - present
Iskenderun Technical University
Position
- Professor (Associate)
October 2020 - June 2022
Iskenderun Technical University
Position
- Professor (Assistant)
March 2018 - October 2020
Iskenderun Technical University
Position
- Lecturer
Education
September 2016 - May 2020
September 2014 - May 2016
September 2010 - June 2014
Publications
Publications (151)
This thesis consists of seventeen chapters. The first chapter is the introduction part which explains the emergence of the theory of post quantum calculus and its historical development. The second chapter includes some definitions, formulas and results belonging to quantum calculus. Some definitions, notations, formulas and results of the (p,q)-ca...
The p-adic numbers are a counterintuitive arithmetic system and were firstly introduced circa end of the nineteenth century. In conjunction with the introduction of these numbers, many mathematicians and physicists started to develop new scientific tools using their available, useful, and applicable properties. Several effects of these researches h...
The main aim of this paper is to introduce the degenerate truncated forms of multifarious special polynomials and numbers and is to investigate their various properties and relationships by using the series manipulation method and diverse special proof techniques. The degenerate truncated exponential polynomials are first considered and their sever...
Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator Dq and divided difference. As applications of the post-quantum calculus known as the (p, q) -calculus, we derive several relations involving the (p, q) -derivative operator and divided differences.
Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, deg...
In recent years, utilizing the generalized quantum exponential function (also known as the (q, h)-exponential function) that extends and unifies the q-and h-exponential functions into a single and convenient form, (q, h)-generalizations of the diverse polynomials and numbers, such as Euler and tangent polynomials and numbers, have been introduced a...
In recent years, utilizing the generalized quantum exponential function (or say (q, h)-exponential function) that unifies, and extends q-and h-exponential functions in an efficient and convenient form, (q, h)-generalizations of the several numbers and polynomials, such as Euler and tangent numbers and polynomials, have been considered and studied....
In this paper, we first review and analyze the Golden integral and its definitions and some properties. Then we introduce a new generalization of the Hermite polynomials via the Golden exponential function (called Fibonacci-Hermite polynomials) and investigate several properties and relations. We derive some explicit and implicit summation formulas...
Recently, the monomiality principle has been extended to q-polynomials, namely, the q-monomiality principle of q-Appell polynomials has been considered. Also, certain results including the monomiality properties of the q-Gould-Hopper polynomials are derived and applications of monomiality are explored for a few members of the q-Appell polynomial fa...
Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families of special numbers and polynomials, such as central Fubini, Bernoulli, central Bell, and Changh...
After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of many families of special polynomials and numbers, such as Bernoulli, Fubini, Bell...
Two new extensions of the familiar Bernoulli polynomials are considered by using q-sine, q-cosine, q-hypergeometric and q-exponential functions. We call q-sine and q-cosine hypergeometric Bernoulli polynomials. Then, diverse formulas and properties for these polynomials, such as summation formulas, addition formulas, q-derivative properties, q-inte...
This study aims to analyze several properties and relations of the degenerate hyper-harmonic numbers and the degenerate harmonic numbers. For this purpose, many identities including the Daehee numbers and derangement numbers, and degenerate Stirling numbers of the first kind are provided. Moreover, the first few values of the degenerate hyper-harmo...
In this work, we consider the degenerate Frobenius-Euler-Genocchi polynomials utilizing the degenerate exponential function and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials utilizing the degenerate logarithm function. Then, we analyze some summation and addition formulas for these polynomials. In addition, we derive some correlation...
The integral transforms play a key role in solving solutions to initial value problems and initial boundary value problems. The integral transform was considered by the French physicists and mathematician P.S. Laplace in 1780, which has very powerful applications, not only in applied mathematics but also in other branches of science such as enginee...
In this study, we consider Boole Genocchi polynomials and derive some useful relations and properties including some summation formulas related to the Boole, Changhee and Genocchi polynomials. Then, we investigate multifarious correlations and formulas including some derivative properties. Also, we acquire diverse implicit summation formulas. Moreo...
In this work, we define Bell-based degenerate Genocchi polynomials of order α. Then we derive diverse correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based degenerate Genocchi polynomials of order α. Moreover, we acquire sev...
Recently, Duran (Degenerate Bell-Hermite-Based Bernoulli Polynomials, SILK ROAD 2. International Scientific Research Congress, 2023) introduced Hermite-Bell-based degenerate Bernoulli polynomials of order α. Then, the author investigated several properties, relations, and identities.
Here, by inspiring and motivating the definitions of Hermite-Bell...
Recently, Araci et al. (Insight into degenerate Bell-based Bernoulli polynomials with applications, in progress, 2023) considered Bell-based degenerate Stirling polynomials of the second kind and derived some useful relations and properties including some summation formulas related to the degenerate Bell polynomials and the degenerate Stirling numb...
Special polynomials and numbers possess much importance in multifarious areas of sciences, such as physics, mathematics, applied sciences, engineering, and other related research fields covering, differential equations, number theory, functional analysis, quantum mechanics, mathematical analysis, mathematical physics, and so on. For example, Bernou...
In this study, we introduce sine and cosine Bell-based Frobenius-type Eulerian polynomials, and by presenting several relations and applications, we analyze certain properties. Our first step is to obtain diverse relations and formulas that cover summation formulas, addition formulas, relations with earlier polynomials in the literature, and differ...
In this paper, the authors introduce a new class of Hermite-based
generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-Genocchi
polynomials. The authors then derive some basic properties and several
implicit summation formulae by utilizing the series manipulation methods.
The authors also investigate several symmetric identities, which are
ext...
The main purpose of this paper is to consider q-sine-based and q-cosine-Based q-Fubini polynomials and is to investigate diverse properties of these polynomials. Furthermore, multifarious correlations including q-analogues of the Genocchi, Euler and Bernoulli polynomials, and the q-Stirling numbers of the second kind are derived. Moreover, some app...
In this study, we consider the truncated degenerate Frobenius-Euler polynomials based on the Gould-Hopper polynomials and examine diverse properties and formulas covering addition formulas, correlations and derivation property. Then, we
derive some interesting implicit summation formulas and symmetric identities. Moreover, we define Gould-Hopper ba...
In this paper, we consider the Gould-Hopper based fully degenerate type2 poly-Euler polynomials with a q parameter and provide some of their properties. Moreover, we derive multifarious correlations and identities for these polynomials, including recurrence relations, symmetric property, and implicit summation formulas.
In this study, by inspiring and motivating the definition of Hermite-Bell based Stirling polynomials of the second kind and the Hermite-Bell based Bernoulli polynomials of order α, we consider Hermite-Bell based Genocchi polynomials of order α and derive some useful relations and properties including some summation formulas related to the Bell poly...
In this study, by inspiring and motivating the definition of Hermite-Bell based Stirling polynomials of the second kind and the Hermite-Bell based Bernoulli polynomials of order α, we consider Hermite-Bell based Stirling polynomials of the first kind and derive some useful relations and properties including some summation formulas related to the Be...
Special polynomials and numbers possess much importance in multifarious areas of sciences, such as physics, mathematics, applied sciences, engineering, and other related research fields covering, differential equations, number theory, functional analysis, quantum mechanics, mathematical analysis, mathematical physics, and so on. For example, Bernou...
In this study, by inspiring and motivating the definition of degenerate truncated Fubini polynomials and the Fubini polynomials of complex variable, we consider degenerate truncated Fubini polynomials of complex variables and derive some useful relations and properties including some summation formulas related to the Fubini polynomials. Then, we in...
In this paper, we consider the degenerate forms of the Catalan–Daehee polynomials and numbers by the Volkenborn integrals and obtain diverse explicit expressions and formulas. Moreover, we show the expressions of the degenerate Catalan–Daehee numbers in terms of λ-Daehee numbers, Stirling numbers of the first kind and Bernoulli polynomials, and we...
In this study, we consider the Gould-Hopper based fully degenerate type2 poly-Genocchi polynomials with a q parameter and provide some of their properties. Moreover, we derive multifarious correlations and identities for these polynomials, including recurrence relations, symmetric property, and implicit summation formulas.
In this study, we introduce Hermite-Bell based Euler polynomials of order and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Hermite-Bell based Euler polynomials of order α. Moreover, we analyze some cas...
In this study, we consider the truncated degenerate Bernoulli polynomials based on the Gould-Hopper polynomials and examine diverse properties and formulas covering addition formulas, correlations and derivation property. Then, we derive some interesting implicit summation formulas and symmetric identities. Moreover, we define Gould-Hopper based tr...
In this paper, the higher-order type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some p-adic integral representations of not only higher-order type 2 Daehee polynomials and numbers but also type 2 Daehee polynomials and numbers are acquired. Several identities and relations related to both centr...
Utilizing p,q-numbers and p,q-concepts, in 2016, Duran et al. considered p,q-Genocchi numbers and polynomials, p,q-Bernoulli numbers and polynomials and p,q-Euler polynomials and numbers and provided multifarious formulas and properties for these polynomials. Inspired and motivated by this consideration, many authors have introduced (p,q)-special p...
In recent years, (p,q)-special polynomials, such as p,q-Euler, p,q-Genocchi, p,q-Bernoulli, and p,q-Frobenius-Euler, have been studied and investigated by many mathematicians, as well physicists. It is important that any polynomial have explicit formulas, symmetric identities, summation formulas, and relations with other polynomials. In this work,...
Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, deg...
In this study, we consider the truncated degenerate Frobenius-Euler polynomials. Then we examine diverse properties and formulas covering addition formulas, correlations and derivation property. Then, we derive some interesting implicit summation formulas.
In this study, we consider the truncated degenerate Euler polynomials based on the Gould-Hopper polynomials and examine diverse properties and formulas covering addition formulas, correlations and derivation property. Then, we derive some interesting implicit summation formulas and symmetric identities. Moreover, we define Gould-Hopper based trunca...
In this study, we consider the truncated degenerate Frobenius-Euler polynomials. Then we examine diverse properties and formulas covering addition formulas, correlations and derivation property. Then, we derive some interesting implicit summation formulas.
In this study, we introduce Bell-based Genocchi polynomials of order and then derive multifarious correlations and formulas including some implicit summation formulas and derivative properties.
In this study, we consider the truncated degenerate sine-Bernoulli polynomials and the truncated degenerate cosine-Bernoulli polynomials. Then we examine diverse properties and formulas covering addition formulas, correlations and derivation property. Also, we derive some interesting implicit summation formulas.
The purpose of this paper is to construct generating function for modified beta polynomials. By utilizing this generating function, we investigate some basic properties of these polynomials. Moreover, we provide several fundamental equations and partial differential equations (PDEs) associated with this generating function.
In this study, we introduce β-extension of Hermite-Bell polynomials and then, investigate some of their porperties and identities. Moreover, we provide two derivative property for these polynomials. Also, we examine some relationships with some well known special polynomials such as Bernoulli, Genocchi and Euler polynomials.
In this paper, we introduce degenerate multi-poly-Bernoulli polynomials and derive some identities of these polynomials. We give
some relationship between degenerate multi-poly-Bernoulli polynomials degenerate Whitney numbers and Stirling numbers of the
first kind. Moreover, we define degenerate multi-poly-Bernoulli polynomials of complex variables...
The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas an...
Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, h...
In this paper, we consider unified Gould-Hopper based Apostol-type polynomials and investigate some of their formulas including several implicit summation formulae and some symmetric identities by the series manipulation method. Moreover, we acquire several new results for unified Gould-Hopper based Apostol-type polynomials using appropriate operat...
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 α and investigate multifarious correlations and formulas...
The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius–Eulerian numbers and polynomials and investigate some of their basic identities and properties including addition theorems, difference equations, derivative properties, recurrence relations. Integral representations, implicit and explicit formulas and relations for the afo...
In the present work, a new extension of the two-variable Fubini polynomials is introduced by means of the polyexponential function, which is called the two-variable type 2 poly-Fubini polynomials. Then, some useful relations including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoull...
Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, h...
The main aim of this paper is to investigate multifarious properties and relations for the gamma
distribution. The approach to reach this purpose will be introducing a special polynomial including
gamma distribution. Several formulas covering addition formula, derivative property, integral
representation, and explicit formula are derived utilizing...
In the present paper, we firstly consider novel q-extensions of the Daehee polynomials named as the generalized twisted q-Daehee polynomials with weight (α,β) and generalized twisted q-Daehee polynomials of the second kind with weight (α,β). For the aforementioned polynomials, we derive various interesting and new formulas and identities covering c...
Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and numbers have been presented and investigated. Motivate...
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...
In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of th...
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...
Inspired by the definition of degenerate multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential functions. In this paper, we consider a class of new generating function for the degenerate multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli polynomials by means of the degenerate multiple p...
In this paper, we first provide the generalized degenerate Gould-Hopper polynomials via thedegenerate exponential functions and then give various relations and formulas such as addition formula andexplicit identity. Moreover, we consider the generalized Gould-Hopper based degenerate central factorialnumbers of the second kind and present several id...
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.
In this paper, a new class of q-Hermite-based Frobenius-type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polyn...
In this paper, we introduce both the generalized degenerate Gould-Hopper based degenerate Stirling polynomials of the second kind and the generalized degenerate Gould-Hopper based fully degenerate Bell polynomials. We study and investigate multifarious properties and relations of these polynomials such as explicit formulas, differentiation rules an...
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...
In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive seve...
We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation method. Multifarious summation formulas and identities given earlier for some well known polynomials such as Eulerian polynomials a...
Diverse relations and identities for p-adic gamma function and p-adic Euler constant by means of weighted p-adic q-integral on p Z and Mahler expansion of the function are investigated. Then several correlations and formulas including the p-adic gamma function, weighted q-Daehee polynomials and weighted q-Daehee polynomials of the second kind are d...
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,...
In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polyn...
The main aim of this paper is to investigate multifarious properties and relations for the gamma distribution. The approach to reach this purpose will be introducing a special polynomial including gamma distribution. Several formulas covering addition formula, derivative property, integral representation and explicit formula are derived by means of...
The main purpose of this paper is to introduce and investigate degenerate Poisson distrib- ution which is a new extension of the Poisson distribution including the degenerate expo- nential function. We then provide several properties of the degenerate Poisson distribution such as the first and the second raw moments and di¤erence operator property....
In the present paper, the (p,q)-Hermite based Apostol type Frobenius-Euler polynomials and numbers are firstly considered and then diverse basic identities and properties for the mentioned polynomials and numbers, including addition theorems, difference equations, integral representations, derivative properties, recurrence relations. Moreover, we p...
In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.
The main aim of this paper is to set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic p-adic integral on Zp. Also, we acquire two fermionic p-adic integrals of p-adic gamma function in...
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...
In this paper, we investigate several relations for p-adic gamma function by means of their Mahler expansion and fermionic p-adic q-integral on Zp. We also derive two fermionic p-adic q-integrals of p-adic gamma function in terms of q-Boole polynomials and numbers. Moreover, we discover fermionic p-adic q-integral of the derivative of p-adic gamma...
We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation method. Multifarious summation formulas and identities given earlier for some well known polynomials such as Eulerian polynomials a...
In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Zp of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of t...
In this paper, we introduce the ρ , q -analog of the p-adic factorial function. By utilizing some properties of ρ , q -numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic ρ , q -gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging...
In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging t...
In this paper, we introduce the two-variable truncated Fubini polynomials and numbers and then investigate many relations and formulas for these polynomials and numbers, including summation formulas, recurrence relations, and the derivative property. We also give some formulas related to the truncated Stirling numbers of the second kind and Apostol...
In this paper, we investigate several relations for p-adic gamma function by means of their Mahler expansion and fermionic p-adic q-integral on ℤ_{p}. We also derive two fermionic p-adic q-integrals of p-adic gamma function in terms of q-Boole polynomials and numbers. Moreover, we discover fermionic p-adic q-integral of the derivative of p-adic gam...
The main aim of this paper is to set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic p-adic integral on ℤ_{p}. Also, we acquire two fermionic p-adic integrals of p-adic gamma function...
In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral o...
The main aim of this paper is to introduce and investigate (p, q)-extensions of two bivariate kinds of Bernoulli polynomials and numbers. We firstly examine several (p, q)-analogues of the Taylor expansions of products of some trigonometric functions and determine their coefficients which are also analyzed in detail. Then, we introduce two bivariat...
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...
In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.
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...
We firstly consider the fully degenerate Gould–Hopper polynomials with a q parameter and investigate some of their properties including difference rule, inversion formula and addition formula. We then introduce the Gould–Hopper-based fully degenerate poly-Bernoulli polynomials with a q parameter and provide some of their diverse basic identities an...
In this paper, we primarily consider a generalization of the fermionic p-adic q-integral on ℤp including the parameters α and β and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of q-Changhee polynomials and numbers as q-Changhee polynomials and numbers with weight (α,β) and q-Changhee p...
In this paper, we first consider the Jacobsthal and Jacobsthal Lucas quaternions and octonions. By making use of definitionsof these sequences, we derive some novel and interesting properties and relations for the Jacobsthal and Jacobsthal Lucas quaternionsand octonions. As universal formulae for these sequences, we obtain the binet formulas. Final...
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...
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...
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...
We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give someof their basic properties including not only addition property, but also derivative properties and integralrepresentations. We also de.ne the Hermite based λ -Stirling polynomials of the second kind, and thenprovide some relations. Moreover, we derive several...
In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Zp of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of t...
We study on the sums of powers of consequtive integers and alternating sums of power of consequtive integers. We derive many identities and correlations including Bernoulli, Euler and Genocchi polynomials and numbers.
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