boole polynomials
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Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 551-558
Author(s):  
Irem Kucukoglu

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.


Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz

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.


Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz

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.


2019 ◽  
Vol 106 (120) ◽  
pp. 105-112
Author(s):  
Ugur Duran ◽  
Mehmet Acikgoz

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.


2016 ◽  
Vol 28 (1-2) ◽  
pp. 279-290 ◽  
Author(s):  
Fatma Gül Gurkan ◽  
Mehmet Acıkgoz ◽  
Erkan Agyuz
Keyword(s):  

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Jongkyum Kwon ◽  
Jin-Woo Park
Keyword(s):  

2015 ◽  
Vol 9 ◽  
pp. 2977-2984
Author(s):  
Taekyun Kim ◽  
Jong Jin Seo
Keyword(s):  

2015 ◽  
Vol 9 ◽  
pp. 4617-4625
Author(s):  
Jin-Woo Park ◽  
Jongkyum Kwon
Keyword(s):  

2014 ◽  
Vol 25 (8) ◽  
pp. 627-633 ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim
Keyword(s):  

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