A note on p -adic q-integral on Z_p associated with q-Euler numbers

Abstract

We show that q-Euler numbers can be represented as an integral by the q-analogue of the ordinary p-adic fermionic measure, whence we give an answer to the question of readers to ask us for the fermionic p-adic q-integral on Zp. In the recent, one reader ask to me that he do not understand for the fermionic integrals I q(f) which was defined in [1]. That is, he told me that he do not understand the definition of I q(f). So, I write this paper to help the reader of my paper. I think that he can understand the definition of I q(f) from this paper.