DC FieldValueLanguage
dc.contributor.authorKotrla, Lukáš
dc.date.accessioned2018-09-21T10:00:13Z-
dc.date.available2018-09-21T10:00:13Z-
dc.date.issued2018
dc.identifier.citationKOTRLA, L. Maclaurin series for sin_p with p an Integer greater than 2. Electronic Journal of Differential Equations, 2018, roč. 135, č. JUL 1 2018, s. 1-11. ISSN: 1072-6691en
dc.identifier.issn1072-6691
dc.identifier.urihttp://hdl.handle.net/11025/29950
dc.format11 s.cs
dc.format.mimetypeapplication/pdf
dc.language.isoenen
dc.publisherTexas State University, Department of Mathematicsen
dc.rightsPlný text je přístupný v rámci univerzity přihlášeným uživatelům.cs
dc.rights© Texas State University, Department of Mathematics-CC-BYen
dc.titleMaclaurin series for sin_p with p an Integer greater than 2en
dc.typečlánekcs
dc.typearticleen
dc.rights.accessrestrictedAccessen
dc.type.versionpublishedVersionen
dc.description.abstract-translatedWe find an explicit formula for the coefficients $\alpha_n$, $n \in \mathbb{N}$, of the generalized Maclaurin series for $\sin_p$ provided $p > 2$ is an integer. Our method is based on an expression of the $n$-th derivative of $\sin_p$ in the form $\sum_{k = 0}^{2^{n - 2} - 1} a_{k,n} \sin_p^{p - 1}(x)\cos_p^{2 - p}(x)\,, \quad x\in \left(0, \frac{\pi_p}{2}\right),$ where $\cos_p$ stands for the first derivative of $\sin_p$. The formula allows us to compute the nonzero coefficients $\alpha_n = \frac{\lim_{x \to 0+} \sin_p^{(np + 1)}(x)}{(np + 1)!}\,.$en
dc.subject.translatedp-Laplacianen
dc.subject.translatedp-trigonometryen
dc.subject.translatedapproximationen
dc.subject.translatedMaclaurin seriesen
dc.subject.translatedcoefficientsen
dc.type.statusPeer-revieweden
dc.identifier.document-number437227300001
dc.identifier.obd43922594
dc.project.IDSGS-2016-003/Kvalitativní a kvantitativní studium matematických modelů III.cs
dc.project.IDLO1506/PUNTIS - Podpora udržitelnosti centra NTIS - Nové technologie pro informační společnostcs
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