Differential and integral equations for the 2-iterated Appell polynomials

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• 作者：Subuhi Khan ; ^{subuhi2006@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Mumtaz Riyasat ^{mumtazrst@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：33E20 ; 33E30
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：306
• 期：Complete
• 页码：116-132
• 全文大小：441 K

文摘

In this article, a set of differential equations of finite order (kth$k\text{th}$ order, k∈N$k\in \mathbb{N}$) for the 2-iterated Appell polynomials are derived. Particular cases k=1$k=1$ and k=2$k=2$ are also considered. The integral equations for the Appell and 2-iterated Appell polynomials are established. Further, as an illustration the differential and integral equations for the 2-iterated generalized Bernoulli polynomials are derived. This article is first attempt in the direction of deriving integral equations for the Appell and 2-iterated Appell families and for some members belonging to these families.