Symbolic computation of some power-trigonometric series. (May 2017)

• Record Type: Journal Article
• Authors: Masjed-Jamei, Mohammad; Koepf, Wolfram
• Is Part Of: Journal of symbolic computation. Volume 80:Part 2(2017)
• Page Start: 273
• Page End: 284
• Publication Date: 2017-05
• Subjects: Bivariate series of power-trigonometric type -- Trigonometric series -- Power series -- Convergence radius; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.03.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Let f ⁎ ( z ) = ∑ j = 0 ∞ a j ⁎ z j be a convergent series in which { a j ⁎ } 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 ∞ a n j + m ⁎ r j cos ⁡ ( α + j ) θ and ∑ j = 0 ∞ a n j + m ⁎ r j sin ⁡ ( α + j ) θ, where r, θ are real variables, α ∈ R, n ∈ N and 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 ) is explicitly given. Three new integral formulae are derived in this direction.