Integer powers of arcsine
Nettet2. jun. 2024 · B.-N. Guo, D. Lim, and F. Qi, Maclaurin's series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula … NettetArcSin can be evaluated to arbitrary numerical precision. ArcSin automatically threads over lists. ArcSin [z] has branch cut discontinuities in the complex plane running from …
Integer powers of arcsine
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Nettet11. apr. 2024 · It was possible in theory. In the previous decade, ESA’s solar-powered Rosetta mission had ventured out to the distance of Jupiter orbit on its mission to rendezvous with a comet – but it had to enter almost total hibernation over 31 months to conserve scarce power. “This was the concern – we were headed to a faraway, dark … Nettet31. mar. 2024 · MacLaurin’s series expansions for positive integer powers of inverse (hyperbolic) sine and tangent functions, closed-form formula of specific partial Bell polynomials, and series representation...
Nettet29. nov. 2024 · Feng [5] proved that the Deshouillers–Dress–Tenenbaum’s arcsine law on divisors of the integers less than x also holds in arithmetic progressions for ``non-exceptional moduli" q\leqslant\exp\ { (\frac {1} {4}-\varepsilon) (\log_2 x)^2\}, where \varepsilon is an arbitrarily small positive number. NettetAlso using pow with integer exponents is not very precise and efficient. However using arctan for this is OK arcsin (x) = arctan (x/sqrt (1- (x*x))); as its Taylor series converges OK on the <0.0,0.8> range all the other parts of the range can be computed through it (using trigonometric identities).
Nettet1. mar. 2024 · From Power Series is Termwise Integrable within Radius of Convergence, (1) can be integrated term by term: We will now prove that the series converges for − 1 … Nettet31. des. 2006 · Integer Powers of Arcsin. Authors. Jonathan M. Borwein; Marc Chamberland; Publication date January 1, 2007. Publisher 'Hindawi Limited' Doi DOI: …
NettetINTEGER POWERS OF ARCSIN AND THE SUM OF SOME SERIES CEZAR LUPU Abstract. In this note, using integer powers of arcsin power series expansion, we generalize an idea of Choe [4] and we provide some new series representations. In particular cases, we recover the famous Euler’s (2). 1. Introduction
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