# A note on the $p$-adic gamma function and $q$-Changhee polynomials

Volume 18, Issue 1, pp 11--17 Publication Date: December 22, 2017       Article History
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### Authors

Özge Çolakoğlu Havare - Mathematics Department, Science and Arts Faculty, Mersin University, 33343, Mersin-Turkey Hamza Menken - Mathematics Department, Science and Arts Faculty, Mersin University, 33343, Mersin-Turkey

### Abstract

In the present work, we consider the fermionic $p$-adic $q$-integral of $p$% -adic gamma function and the derivative of $p$-adic gamma function by using their Mahler expansions. The relationship between the $p$-adic gamma function and $% q$-Changhee numbers is obtained. A new representation is given for the $p$-adic Euler constant. Also, we study on the relationship between $q$-Changhee polynomials and $p$-adic Euler constant using the fermionic $p$-adic $q$-integral techniques the idea that the $q$-Changhee polynomial.

### Keywords

• $p$-Adic number
• $p$-adic gamma function
• the fermionic $p$-adic $q$-integral
• Mahler coefficients
• $p$-adic Euler constant
• $q$-Changhee Polynomials

•  11S80
•  05A30
•  33E50
•  05A19
•  26C05

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