Symmetry Fermionic p-Adic q-Integral on ℤp for Eulerian Polynomials

Abstract EN

Kim et al.

(2012) introduced an interesting p-adic analogue of the Eulerian polynomials.

They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers.

In this paper, by applying the symmetry of the fermionic p-adic q-integral on ℤp, defined by Kim (2008), we show a symmetric relation between the q-extension of the alternating sum of integer powers and the Eulerian polynomials.