Symbolic computation of some power-trigonometric series

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• 作者：Mohammad Masjed-Jamei^a ; ^{mmjamei@kntu.ac.ir} ; ^{mmjamei@yahoo.com} ; Wolfram Koepf^b ; ^{koepf@mathematik.uni-kassel.de}
• 关键词：Bivariate series of power-trigonometric type ; Trigonometric series ; Power series ; Convergence radius
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：May-June 2017
• 年：2017
• 卷：80
• 期：part_P2
• 页码：273-284
• 全文大小：275 K
• 卷排序：80

文摘

Let f⁎(z)=∑j=0∞aj⁎zj be a convergent series in which {aj⁎}j=0∞ are known real numbers. In this paper, by referring to Osler's lemma (Osler, 1975), we obtain explicit forms of the two bivariate series∑j=0∞anj+m⁎rjcos⁡(α+j)θand∑j=0∞anj+m⁎rjsin⁡(α+j)θ, where r, θ   are real variables, α∈Rα∈R, n∈Nn∈N and m∈{0,1,…,n−1}m∈{0,1,…,n−1}. With some illustrative examples, we also show how to obtain the explicit form of a trigonometric series when f⁎(z)f⁎(z) is explicitly given. Three new integral formulae are derived in this direction.