含参数a，b，c的高阶Apostol型Poly-Genocchi多项式
Higher Order Apostol-Type Poly-Genocchi Polynomials with Parameters a, b and c
摘要：
本文利用多重对数定义了一种新形式的多Genocchi多项式，即带参数a，b，c的Apostol型高阶多Genocchi多项式。建立了这类多项式的一些性质，包括用第二类Stirling数、高阶Apostol型Bernoulli多项式和高阶Frobenius多项式表示高阶Apostol型poly-Genocchi多项式的递推关系和显式公式.此外，还得到了一定的微分恒等式，使得这种新形式的poly-Genocchi多项式被归为Appell多项式，从而利用Appell多项式的一些定理得到了更多的性质.此外，这种新形式的poly-Genocchi多项式的对称化推广，具有双重生成函数。最后，利用多指数函数的概念定义了参数为a，b，c的2型Apostol-poly-Genocchi多项式，并导出了几个恒等式，其中两个恒等式表明了这些多项式与第一类Stirling数和2型Apostol型poly-伯努利多项式的关系.
英文摘要：
In this paper, a new form of poly-Genocchi polynomials is defined by means of poly-logarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are established including some recurrence relations and explicit formulas, which express these higher order Apostol-type poly-Genocchi polynomials in terms of Stirling numbers of the second kind, Apostol-type Bernoulli and Frobenius polynomials of higher order. Moreover, certain differential identity is obtained that leads this new form of poly-Genocchi polynomials to be classified as Appell polynomials and, consequently, draw more properties using some theorems on Appell polynomials. Furthermore, a symmetrized generalization of this new form of poly-Genocchi polynomials is introduced that possesses a double generating function. Finally, the type 2 Apostol-poly-Genocchi polynomials with parameters a, b and c are defined using the concept of polyexponential function and several identities are derived, two of which show the connections of these polynomials with Stirling numbers of the first kind and the type 2 Apostol-type poly-Bernoulli polynomials.
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