Name
Abstract | ||
|---|---|---|
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∈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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.jsc.2016.03.004 | Journal of Symbolic Computation |
Keywords | Field | DocType |
Bivariate series of power-trigonometric type,Trigonometric series,Power series,Convergence radius | Trigonometric series,Discrete mathematics,Combinatorics,Symbolic computation,Power series,Real number,Convergent series,Lemma (mathematics),Mathematics | Journal |
Volume | ISSN | Citations |
80 | 0747-7171 | 0 |
PageRank | References | Authors |
0.34 | 2 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammad Masjed-Jamei | 1 | 15 | 8.03 |
| Wolfram Koepf | 2 | 84 | 20.19 |