Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials - Daeyeoul Kim; Min-Soo Kim (International Journal of Mathematics and Mathematical Sciences)
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.