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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, an experimental comparison study of two quantization methods, namely uniform sensitivity quantization and minimum expected spectral deviation quantization, was conducted. But the results showed that moderate to substantial bit savings can be obtained by using the minimum deviation method which embeds parameter probability density information into the quantization process.
Abstract: Based upon the theoretical development of a recent paper on scalar parameter quantization of speech reflection coefficients, an experimental comparison study of two quantization methods was undertaken. The first method, called uniform sensitivity quantization, makes use of measured sensitivity data from speech parameters to obtain quantization tables. Log area and inverse sine transformation followed by uniform quantization are examples of approaches which are considered in this category (with the inverse sine approach theoretically resulting in the uniform sensitivity solution). The second method is called minimum expected spectral deviation or minimum deviation quantization. This approach theoretically makes use of the probability density of each parameter in addition to the parameter sensitivity. A practical implementation of this method is presented here along with computer programs and then a comparison with the uniform sensitivity method is given. Quantitative results and subjective evaluation by an experienced listener indicate that moderate to substantial bit savings can be obtained by using the minimum deviation method which embeds parameter probability density information into the quantization process.

12 citations

Book ChapterDOI
08 Jul 2013
TL;DR: This work has made explicit and implemented techniques for calculating the cuts in the computer algebra programme Maple, and gathered them in the BranchCuts package, along with tools for visualising the cuts.
Abstract: We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse trigonometric functions. Understanding these cuts is essential for working with the single-valued counterparts, the common approach to encoding multi-valued functions in computer algebra systems. While the defining choices are usually simple (typically portions of either the real or imaginary axes) the cuts induced by the expression may be surprisingly complicated. We have made explicit and implemented techniques for calculating the cuts in the computer algebra programme Maple. We discuss the issues raised, classifying the different cuts produced. The techniques have been gathered in the BranchCuts package, along with tools for visualising the cuts. The package is included in Maple 17 as part of the FunctionAdvisor tool.

12 citations

Journal ArticleDOI
TL;DR: Several new closed formulas for higher- order derivatives of trigonometric and hyperbolic functions are found, a higher-order convolution formula is derived for the tangent numbers, and a recurrence relation is generalized for the Tangent numbers.

11 citations

Journal ArticleDOI
TL;DR: In this article, the properties of q-exponential and q-trigonometric functions were examined and discussed in the literature, and it was shown that they are related to Jackson's q-analogues of the exponential and trigonometric functions by classical Fourier - Gauss transformations.
Abstract: We examine the properties of q-exponential and q-trigonometric functions, recently introduced and discussed in the literature. It is shown that they are related to Jackson's q-analogues of the exponential and trigonometric functions by classical Fourier - Gauss transformations.

11 citations

Journal ArticleDOI
TL;DR: Several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms have been presented in this article, which are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions.

11 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202335
202298
202134
202027
201918
201814