Some series identities involving the generalized Apostol type and related polynomials
Some series identities involving the generalized Apostol type and related polynomials
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DOI：
10.1016/j.camwa.2011.09.010
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发表时间：
2011-11
期刊：
影响因子：
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通讯作者：
Da-qian Lu;Hari M. Srivastava
中科院分区：
文献类型：
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作者：
Da-qian Lu;Hari M. Srivastava
最近，Luo和Srivastava [Q.-]引入并研究了各种Apostol型多项式的统一（和推广）。罗明，斯里瓦斯塔瓦，Apostol-Genocchi多项式和第二类斯特林数的一些推广，应用数学计算。217（2011）5702-5728]。本文利用广义Apostol型多项式的生成函数证明了它们的几个对称恒等式。作为我们结果的特殊情况和推论，我们得到了高阶Apostol-Euler多项式、高阶Apostol-Bernoulli多项式和高阶Apostol-Genocchi多项式以及Ozden等人系统研究的另一类广义Apostol型多项式的相应对称恒等式. [H. Ozden，Y. Simsek，H.M. Srivastava，广义Bernoulli，Euler和Genocchi多项式的生成函数的统一表示，Comput. 60（2010）2779-2787]。我们还得到了Apostol型多项式、广义整数幂和与广义交错和之间的几个关系。它展示了这些结果中的每一个如何扩展相应的已知身份。
A unification (and generalization) of various Apostol type polynomials was introduced and investigated recently by Luo and Srivastava [Q.-M. Luo, H.M. Srivastava, Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput. 217 (2011) 5702–5728]. In this paper, we prove several symmetry identities for these generalized Apostol type polynomials by using their generating functions. As special cases and consequences of our results, we obtain the corresponding symmetry identities for the Apostol–Euler polynomials of higher order, the Apostol–Bernoulli polynomials of higher order and the Apostol–Genocchi polynomials of higher order, and also for another family of generalized Apostol type polynomials which were investigated systematically by Ozden et al. [H. Ozden, Y. Simsek, H.M. Srivastava, A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl. 60 (2010) 2779–2787]. We also derive several relations between the Apostol type polynomials, the generalized sum of integer powers and the generalized alternating sum. It is shown how each of these results would extend the corresponding known identities.