Araci Serkan, Khan Waseem A, Acikgoz Mehmet, Özel Cenap, Kumam Poom
Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, 27410 Gaziantep, Turkey.
Department of Mathematics, Integral University, Lucknow, 226026 India.
Springerplus. 2016 Jun 24;5(1):860. doi: 10.1186/s40064-016-2357-4. eCollection 2016.
By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite-Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679-695, 2015a) and Hermite-Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite-Genocchi polynomials defined in this paper.
通过使用Araci等人（《应用数学与信息科学》8(6):2803 - 2808, 2014）给出的修正米尔恩 - 汤姆森多项式，我们引入了阿波斯托尔埃尔米特 - 热诺奇多项式的一个新概念。我们还对上述多项式进行了进一步研究，并通过不同的分析方法和生成函数法推导出一些隐式求和公式和一般对称恒等式。这里得到的结果是将埃尔米特 - 伯努利多项式（Pathan和Khan，《地中海数学杂志》12:679 - 695, 2015a）以及埃尔米特 - 欧拉多项式（Pathan和Khan，《地中海数学杂志》2015b，doi:10.1007/s00009 - 015 - 0551 - 1）扩展到本文所定义的阿波斯托尔型埃尔米特 - 热诺奇多项式。
