The volkenborn integral of the 𝒑-adic gamma function

Havare, Özge Çolakoğlu; Menken, Hamza

doi:10.21833/ijaas.2018.02.009

Cited by 8 publications

(9 citation statements)

References 18 publications

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“…It is easy to show that lim q!1 [x] q = x for any x with jxj p 1 in the p-adic case (for details, cf. [1][2][3][4][5][6][7][8][9][10]; see also the related references cited therein).…”

Section: Introductionmentioning

confidence: 99%

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

Duran¹,

Açıkgöz²

2019

Preprint

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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.

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“…It is easy to show that lim q!1 [x] q = x for any x with jxj p 1 in the p-adic case (for details, cf. [1][2][3][4][5][6][7][8][9][10]; see also the related references cited therein).…”

Section: Introductionmentioning

confidence: 99%

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

Duran¹,

Açıkgöz²

2019

Preprint

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“…Therefore, in the recent forty years, p-adic gamma function and its generalizations have been investigated and studied extensively by many mathematicians (cf. [1][2][3][4][5][6][7][8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

“…These functions have been studied and investigated by many mathematicians, see [3][4][5][6][7][8][9]11,12]. The (ρ, q)-numbers are defined by…”

Section: Introductionmentioning

confidence: 99%

A Study on Novel Extensions for the p-adic Gamma and p-adic Beta Functions

Duran

Açıkgöz

2019

MCA

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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 to the foregoing gamma function, some of which are given for the case p = 2 . We also derive more representations of the p-adic ρ , q -gamma function in general case. Moreover, we consider the p-adic ρ , q -Euler constant derived from the derivation of p-adic ρ , q -gamma function at x = 1 . Furthermore, we provide a limit representation of aforementioned Euler constant based on ρ , q -numbers. Finally, we consider ρ , q -extension of the p-adic beta function via the p-adic ρ , q -gamma function and we then investigate various formulas and identities.

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“…The normalized absolute value according to the theory of p-adic analysis is given by jpj p = p 1 (for details, cf. [1][2][3][4][5][6][7][8][9][10][11][12]; see also the related references cited therein).…”

Section: Introductionmentioning

confidence: 99%

<strong></strong>The Boole Polynomials Associated with the p-adic Gamma Function

Duran

Açıkgöz

2019

Preprint

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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.

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The volkenborn integral of the 𝒑-adic gamma function

Abstract: In the present work the -adic gamma function has been considered. The Volkenborn integral of the -adic gamma function by using its Mahler expansion has been derived. Moreover, a new representation for the -adic Euler constant has been given.

Cited by 8 publications

References 18 publications

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

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

A Study on Novel Extensions for the p-adic Gamma and p-adic Beta Functions

<strong></strong>The Boole Polynomials Associated with the p-adic Gamma Function

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