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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01 Jan 1982TL;DR: A synthesis principle applied to a monolithic circuit capable of generating trigonometric functions (sine, cosine, tangent, cosecant, secant and cotangent, plus arctangent) is presented in this paper.
Abstract: A synthesis principle applied to a monolithic circuit capable of generating trigonometric functions (sine, cosine, tangent, cosecant, secant and cotangent, plus arctangent) will be Presented. Analog inputs represent angle and amplitude. Law conformance is as close as ∓ 0.02%.
5 citations
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TL;DR: In this article, the authors used rational functions, logarithms and inverse trigonometric functions to construct closed-form expressions of the Voigt function K (x, y ) in terms of rational functions and showed that these expressions are not competitive with other algorithms with respect to computational speed.
Abstract: Rational approximations for the Gauss function can be used to construct closed-form expressions of the Voigt function K ( x, y ) in terms of rational functions, logarithms and inverse trigonometric functions. The comparison with accurate reference values indicates a relative accuracy in the percent range for y ≳ 1, but serious problems for smaller y . Furthermore, these expressions are not competitive with other algorithms with respect to computational speed. Both accuracy and speed tests indicate that supposedly “good” approximations of the integrand do not necessarily provide good approximations of the integral, i.e. Voigt function.
5 citations
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23 Apr 1988
TL;DR: In this paper, the phase of the color burst signal is shifted at 90 deg. or $090 deg. by a -90 deg. phase shifter 4, and the output signal of the phase shiftter 4 is divided by the input color burst signals in a divider 5, and output signal is subjected to inverse trigonometric function arithmetic by a tan inverse trigonal function arithmetic unit 6, while the difference between the output signals of the unit 6 and that of the delay circuit 7 is operated by an adder 8 to obtain the AFC signal.
Abstract: PURPOSE:To lead out an AFC signal, an APC signal, and an ACC signal at a high speed and to simplify the circuit constitution by subjecting an input color burst signal to prescribed arithmetic. CONSTITUTION:The phase of the color burst signal is shifted at 90 deg. or $090 deg. by a -90 deg. phase shifter 4, and the output signal of the phase shifter 4 is divided by the input color burst signal in a divider 5, and the output signal of the divider 5 is subjected to inverse trigonometric function arithmetic by a tan inverse trigonometric function arithmetic unit 6, and the output signal of the unit 6 is delayed in ahone clock delay circuit 7 by one sampling period, and the difference between te output signal of the unit 6 and that of the delay circuit 7 is operated by an adder 8 to obtain the AFC signal. The output signal of the unit 6 is subjected to trigonometric function arithmetic in an sin trigonometric function arithmetic unit 10, and the output signal of the unit 10 is divided by the input color burst signal or the output signal of the phase shifter 4 in a divider 11 to obtain the ACC signal. The difference of phase between the output signal of the unit 6 and a reference signal is operated by an adder 18 to obtain the APC signal.
5 citations
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26 Jan 2021
TL;DR: In this paper, the nice Maclaurin series expansions and series identities for powers of the inverse sine function and the inverse hyperbolic tangent function have been established, in terms of the first kind Stirling numbers, binomial coefficients and multiple sums.
Abstract: In the paper, the authors establish nice Maclaurin series expansions and series identities for powers of the inverse sine function, for powers of the inverse hyperbolic sine function, for composites of incomplete gamma functions with the inverse hyperbolic sine function, for powers of the inverse tangent function, and for powers of the inverse hyperbolic tangent function, in terms of the first kind Stirling numbers, binomial coefficients, and multiple sums, apply the nice Maclaurin series expansion for powers of the inverse sine function to derive an explicit formula for special values of the second kind Bell polynomials and to derive a series representation of the generalized logsine function, and deduce several combinatorial identities involving the first kind Stirling numbers. Some of these results simplify and unify some known ones.
5 citations
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TL;DR: This work provides human-accessible Buffon machines, which require a dozen coin flips or less, on average, and produces experiments whose probabilities of success are expressible in terms of numbers such as π, exp(−1), log2, √3, cos(1/4), ζ(5).
Abstract: The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/pi ~ 0.63661, which is the experiment's probability of success. Generalizing the experiment and simplifying the computational framework, we consider probability distributions, which can be produced perfectly, from a discrete source of unbiased coin flips. We describe and analyse a few simple Buffon machines that generate geometric, Poisson, and logarithmic-series distributions. We provide human-accessible Buffon machines, which require a dozen coin flips or less, on average, and produce experiments whose probabilities of success are expressible in terms of numbers such as, exp(-1), log 2, sqrt(3), cos(1/4), aeta(5). Generally, we develop a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms, polylogarithms, direct and inverse trigonometric functions, algebraic and hypergeometric functions, as well as functions defined by integrals, such as the Gaussian error function.
5 citations