A note on the \(p\)-adic gamma function and \(q\)-Changhee polynomials


Authors

Özge Çolako─člu 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.


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