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标题：Symmetry Fermionic <svg style="vertical-align:-3.294pt;width:11.0875px;" id="M1" height="14.1125" version="1.1" viewBox="0 0 11.0875 14.1125" width="11.0875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1125)"> <g transform="translate(72,-60.71)"> <text transform="matrix(1,0,0,-1,-71.95,64.04)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑝</tspan> </text> </g> </g> </svg>-Adic <svg style="vertical-align:-3.294pt;width:11.2875px;" id="M2" height="14.1125" version="1.1" viewBox="0 0 11.2875 14.1125" width="11.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.1125)"> <g transform="translate(72,-60.71)"> <text transform="matrix(1,0,0,-1,-71.95,64.04)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑞</tspan> </text> </g> </g> </svg>-Integral on <svg style="vertical-align:-6.80586pt;width:24.7125px;" id="M3" height="23.4375" version="1.1" viewBox="0 0 24.7125 23.4375" width="24.7125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,23.4375)"> <g transform="translate(72,-53.25)"> <text transform="matrix(1,0,0,-1,-71.95,60.08)"> <tspan style="font-size: 17.93px; " x="0" y="0">ℤ</tspan> </text> <text transform="matrix(1,0,0,-1,-58.91,55.6)"> <tspan style="font-size: 12.55px; " x="0" y="0">𝑝</tspan> </text> </g> </g> </svg> for Eulerian Polynomials
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作者：Daeyeoul Kim ; Min-Soo Kim
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2012
卷号：2012
DOI：10.1155/2012/424189
出版社：Hindawi Publishing Corporation
摘要：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.