scholarly journals On Mahler Expansion of p-adic Gamma Function Affiliated with the q-Boole Polynomials

2019 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Gamma Function ◽  
Stirling Numbers ◽  
Euler Constant ◽  
Boole Polynomials

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 gamma function. We acquire a representation for the p-adic Euler constant by means of the q-Boole polynomials. We finally develop a novel, explicit and interesting representation for the p-adic Euler constant including Stirling numbers of the first kind.

scholarly journals The Boole polynomials associated with the p-adic gamma function

2019 ◽  
Vol 106 (120) ◽  
pp. 105-112
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Gamma Function ◽  
Stirling Numbers ◽  
Explicit Representation ◽  
Euler Constant ◽  
Boole Polynomials

We 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 terms of Boole numbers and polynomials. We then provide fermionic p-adic integral of the derivative of p-adic gamma function and a representation for the p-adic Euler constant by means of the Boole polynomials. Furthermore, we investigate an explicit representation for the aforesaid constant covering Stirling numbers of the first kind.

scholarly journals The Boole Polynomials Associated with the p-adic Gamma Function

2019 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Gamma Function ◽  
Stirling Numbers ◽  
Explicit Representation ◽  
Euler Constant ◽  
Boole Polynomials

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 terms of Boole numbers and polynomials. We then provide fermionic p-adic integral of the derivative of p-adic gamma function and a representation for the p-adic Euler constant by means of the Boole polynomials. Furthermore, we investigate an explicit representation for the aforesaid constant covering Stirling numbers of the first kind.

On applications for Mahler expansion associated with p-adic q-integrals

2019 ◽  
Vol 15 (01) ◽  
pp. 67-84 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Explicit Formula ◽  
Gamma Function ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Symmetric Relation ◽  
Euler Constant ◽  
Basic Properties ◽  
Changhee Polynomials

In this paper, we primarily consider a generalization of the fermionic [Formula: see text]-adic [Formula: see text]-integral on [Formula: see text] including the parameters [Formula: see text] and [Formula: see text] and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of [Formula: see text]-Changhee polynomials and numbers as [Formula: see text]-Changhee polynomials and numbers with weight [Formula: see text] and [Formula: see text]-Changhee polynomials and numbers of second kind with weight [Formula: see text]. For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted [Formula: see text]-Euler polynomials, [Formula: see text]-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted [Formula: see text]-Changhee polynomials and [Formula: see text]-adic gamma function. Also, we compute the weighted fermionic [Formula: see text]-adic [Formula: see text]-integral of the derivative of [Formula: see text]-adic gamma function. Moreover, we give a novel representation for the [Formula: see text]-adic Euler constant by means of the weighted [Formula: see text]-Changhee polynomials and numbers. We finally provide a quirky explicit formula for [Formula: see text]-adic Euler constant.

scholarly journals On p-adic Gamma Function Related to q-Daehee Polynomials and Numbers

2019 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Gamma Function ◽  
Stirling Numbers ◽  
Euler Constant ◽  
The Relationship

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 of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

scholarly journals Some Relationships Including p-Adic Gamma Function and q-Daehee Polynomials and Numbers

2018 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Gamma Function ◽  
Stirling Numbers ◽  
Euler Constant ◽  
The Relationship

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 the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

scholarly journals New results on the q-generalized Bernoulli polynomials of level m

2019 ◽  
Vol 52 (1) ◽  
pp. 511-522
Author(s):  
Alejandro Urieles ◽  
María José Ortega ◽  
William Ramírez ◽  
Samuel Vega
Keyword(s):  
Gamma Function ◽  
Bernstein Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Algebraic Properties ◽  
Generalized Bernoulli Polynomials ◽  
Polynomial Class

AbstractThis paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.

scholarly journals Relationships between Mahler Expansion and Higher Order q-Daehee polynomials

2019 ◽  
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz
Keyword(s):  
Gamma Function ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Higher Order

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.

scholarly journals On a generalization of Euler constant in connection to di-Gamma function

2012 ◽  
Vol 21 (1) ◽  
pp. 13-20
Author(s):  
LASZLO BALOG ◽  
Keyword(s):  
Gamma Function ◽  
Euler’S Constant ◽  
Euler Constant ◽  
Appl Math ◽  
Euler's Constant

In this paper we study the sequences {xn}, {yn} defined for each n ≥ 1 by ... , in connection to Gamma and di-Gamma function. Our results generalize some previous ones in [Berinde, V. A new generalization of Euler’s constant, Creat. Math.Inform. 18 (2009), No. 2, 123–128] and [Sant ˆ am˘ arian, A., ˘ A generalization of Euler constant, Mediamira, Cluj-Napoca, 2008] and are inspired from the paper [Mortici, C., Improved convergence towards generalized Euler-Mascheroni constant, Appl. Math. Comput., 2009, doi: 10.1016/j.amc.2009.10.039].

scholarly journals Some new identities and formulas for higher-order combinatorial-type numbers and polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 551-558
Author(s):  
Irem Kucukoglu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Higher Order ◽  
Combinatorial Type ◽  
Derivative Formulas ◽  
Cauchy Numbers ◽  
Special Numbers And Polynomials ◽  
Boole Polynomials ◽  
Changhee Numbers

The main purpose of this paper is to provide various identities and formulas for higherorder combinatorial-type numbers and polynomials with the help of generating functions and their both functional equations and derivative formulas. The results of this paper comprise some special numbers and polynomials such as the Stirling numbers of the first kind, the Cauchy numbers, the Changhee numbers, the Simsek numbers, the Peters poynomials, the Boole polynomials, the Simsek polynomials. Finally, remarks and observations on our results are given.

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