Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4945959 | Journal of Symbolic Computation | 2017 | 14 Pages |
Abstract
Let fâ(z)=âj=0âajâzj be a convergent series in which {ajâ}j=0â are known real numbers. In this paper, by referring to Osler's lemma (Osler, 1975), we obtain explicit forms of the two bivariate seriesâj=0âanj+mârjcosâ¡(α+j)θandâj=0âanj+mârjsinâ¡(α+j)θ, where r, θ are real variables, αâR, nâN and mâ{0,1,â¦,nâ1}. With some illustrative examples, we also show how to obtain the explicit form of a trigonometric series when fâ(z) is explicitly given. Three new integral formulae are derived in this direction.
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Authors
Mohammad Masjed-Jamei, Wolfram Koepf,