Topic
Inverse trigonometric functions
About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.
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TL;DR: A new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems based on fitting functions that are trigonometric (rather than algebraic as in classical integrators).
38 citations
TL;DR: A new algorithm for computing the complex logarithm and exponential functions is proposed, based on shift-and-add elementary steps, and it generalizes some algorithms by Briggs and De Lugish (1970), as well as the CORDIC algorithm.
Abstract: A new algorithm for computing the complex logarithm and exponential functions is proposed. This algorithm is based on shift-and-add elementary steps, and it generalizes some algorithms by Briggs and De Lugish (1970), as well as the CORDIC algorithm. It can easily be used to compute the classical real elementary functions (sin, cos, arctan, ln, exp). This algorithm is more suitable for computations in a redundant number system than the CORDIC algorithm, since there is no scaling factor when computing trigonometric functions. >
37 citations
TL;DR: The trigonometric functions did not enter calculus until about 1739 as mentioned in this paper, and no textbook until 1748 dealt with the calculus of these functions, and no calculus texts written in England and the continent during the first half of the 18th century was there a treatment of the derivative and integral of the sine or cosine or any discussion of the periodicity or addition properties of the functions.
35 citations
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TL;DR: In this article, the eigenfunctions of the one-dimensional $p$-Laplace operator, the $\sin_p$ functions, and prove several inequalities for these and other trigonometric functions and their inverse functions.
Abstract: Motivated by the work of P. Lindqvist, we study eigenfunctions of the one-dimensional $p$-Laplace operator, the $\sin_p$ functions, and prove several inequalities for these and $p$-analogues of other trigonometric functions and their inverse functions. Similar inequalities are given also for the $p$-analogues of the hyperbolic functions and their inverses.
34 citations
TL;DR: A multiresolution analysis of nested subspaces of trigonometric polynomials of Hermite interpolation on a dyadic partition of nodes on the interval [0,2π].
Abstract: The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval [0,2π]. Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.
34 citations