欧拉多项式的新推广及其应用
New Generalization of Eulerian polynomials and their applications
摘要：
本文引入了带a、b参数的欧拉多项式，并给出了它们的定义。利用多项式母函数的定义，得到了解析数论中的一些新恒等式。给出了带a、b参数的欧拉多项式、伯恩斯坦多项式、多对数函数、Bernoulli数和欧拉数之间的关系。此外，我们看到，我们的多项式在a =-1相关的欧拉-泽塔函数在负整数。最后，我们得到了本文所表达的欧拉多项式的新推广的Witt公式。
英文摘要：
In the present paper, we introduce Eulerian polynomials with a and b parameters and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Theory of Analytic Numbers. Also, we give relations between Eulerian polynomials with a and b parameters, Bernstein polynomials, Poly-logarithm function, Bernoulli numbers and Euler numbers. Moreover, we see that our polynomials at a =-1 are related to Euler-Zeta function at negative inetegers. Finally, we get Witt's formula for new generalization of Eulerian polynomials which we express in this paper.
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