Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
Open Access
Journal Browser
Turkish Journal of Analysis and Number Theory. 2018, 6(4), 120-123
DOI: 10.12691/tjant-6-4-3
Open AccessArticle

On the p-adic Gamma Function and Changhee Polynomials

Özge Çolakoğlu Havare1, and Hamza Menken1

1Mersin University, Science and Arts Faculty, Mathematics Department, 33343, Mersin, Turkey

Pub. Date: August 28, 2018

Cite this paper:
Özge Çolakoğlu Havare and Hamza Menken. On the p-adic Gamma Function and Changhee Polynomials. Turkish Journal of Analysis and Number Theory. 2018; 6(4):120-123. doi: 10.12691/tjant-6-4-3


The p-adic gamma function is considered to obtain its derivative and to evaluate its the fermionic p-adic integral. Furthermore the relationship between the p-adic gamma function and Changhee polynomials and also between the Changhee polynomials and p-adic Euler constants is obtained. In addition, the p-adic Euler constants are expressed in term of Mahler coefficients of the p-adic gamma function.

p-adic number p-adic gamma function the fermionic p-adic integral Mahler coefficients p-adic Euler constant Changhee Polynomials

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/


[1]  I. V. Volovich, Number theory as the ultimate physical theory, Preprint No. TH 4781/87, CERN, Geneva, (1987).
[2]  V. S Vladimirov and I. V. Volovich, Superanalysis. I. Differential calculus, Theor. Math. Phys. 59, (1984) 317.335.
[3]  S. Araci, E. Ağyüz, M. Acikgoz, On a q-analogue of some numbers and polynomials, J. Inequal. Appl. (2015) 2015: 19.
[4]  S. Araci and M. Acikgöz, A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbers, Adv. Diffierence Equa., (2015) 2015: 30.
[5]  I. N. Cangul, A. S. Cevik, Y. Simsek, Generalization of q-Apostol-type Eulerian numbers and polynomials, and their interpolation functions, Adv. Stud. Contemp. Math. 25 (2) (2015), 211-220.
[6]  Y. Simsek, Special Numbers on Analytic Functions, Applied Mathematics, (2014), 5, 1091-1098.
[7]  H. Srivastava, B. Kurt, Y. Simsek, Some Families of Genocchi Type Polynomials And Their Interpolation Functions, Integral Transforms and Special Functions, no.12, ( 2012), 919-938.
[8]  H. M. Srivastava, T. Kim, Y. Simsek, q-Bernoulli numbers and polynomials associated with multiple q-zeta functions and basic L-series. Russ. J. Math. Phys., (2005), 12, 241-268.
[9]  S. Araci, D. Erdal, J. J. Seo, A study on the fermionic p-adic q-integralrepresentation on associated with weighted q-Bernstein and q-Genocchi polynomials, Abstr. Appl. Anal. 2011 (2011) Article ID 649248, 10 pp.
[10]  T. Kim, On the analogs of Euler numbers and polynomials associated with p-adic q-integral on at q = -1, J. Math. Anal. Appl., 331 (2007) pp 779-792.
[11]  T. Kim. q-Volkenborn integration, Russian Journal of Mathematical Physics, vol. 9, no.3, (2002) pp. 288.299.
[12]  T. Kim, Symmetry of power sum polynomials and multivariate fermionic p-adic invariant integral on , Russ. J. Math. Phys. 16 (1), (2009), 93-96.
[13]  H. Ozden, I.N. Cangul and Y. Simsek, Generalized q-Stirling Numbers and Their Interpolation Functions. Axioms (2013), 2, 10-19.
[14]  Y. Simsek, A. Yardimci, Applications on the Apostol-Daehe numbers and polynomials as-sociated with special numbers, polynomials, and p-adic integrals, Advances in Difference Equations (2016), 2016: 308.
[15]  Y. Simsek, Analysis of the p-adic q-Volkenborn integrals: An approach to generalized Apostol-type special numbers and polynomials and their applications, Cogent Mathematics, (2016), 3: 1269393.
[16]  Y. Morita, A p-adic analogue of the Γ-function, J. Fac. Science Univ., 22 (1975), 225-266.
[17]  J. Diamond, The p-adic log gamma function and p-adic Euler constant, Trans. Amer. Math. Soc. 233 (1977), 321-337.
[18]  D. Barsky, On Morita’s p-adic gamma Function, Groupe d’Etude d’Analyse Ultramétrique, 5 (1977/78), 3, 1-6.
[19]  B. Dwork, A note on p-adic gamma function, Groupe de travail d’analyse ultramétrique, 9 (1981-1982), 3, J1-J10.
[20]  W. H. Schikhof, Ultrametric Calculus: An Introduction to p-adic Analysis, Cambridge University Pres, 1984.
[21]  K. Mahler, An Interpolation Series for Continuous Functions of a p-adic Variable, J. Reine Angew. Math., 199, (1958) 23-34.
[22]  A. M. Robert, A Course in p-adic Analysis, Graduate Texts in Mathematics 198, Springer, 2000.
[23]  T. Kim, D. S. Kim, Mansour, T., Rim, S. H., Schork, M., Umbral calculus and Sheffer sequences of polynomials, J. Math. Phys. 54, 083504 (2013).
[24]  D. S. Kim, T. Kim, J. Seo, A note on Changhee Polynomials and Numbers, Adv. Studies Theor. Phys., vol. 7, no.20, (2013) 993-1003.