Question

How to calculate $\arcsin$ of dual number: $\arcsin\left( x+y\cdot\varepsilon\right)$ where $x,y\in\mathbb{R}$ and $\varepsilon\ne0=\varepsilon^{2}$?

score 95 · Answer 1 · 2023-02-04 05:22:36

How to calculate $\arcsin$ of dual number: $\arcsin\left( x+y\cdot\varepsilon\right)$ where $x,y\in\mathbb{R}$ and $\varepsilon\ne0=\varepsilon^{2}$?

score 107 · Answer 2 · 2023-02-14 20:41:08

107

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Function to approximate infinite series $\sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n+1)!}$

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score 43 · Answer 3 · 2023-03-12 03:30:08

43

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Possibility of computing antiderivative using dual numbers

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score 203 · Answer 4 · 2023-04-07 14:56:42

203

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Have generalisations of dual numbers/complex numbers/quaternions/octonions... been studied?

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score 63 · Answer 5 · 2023-04-09 14:05:44

63

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score 131 · Answer 6 · 2023-06-18 16:43:37

131

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score 67 · Answer 7 · 2023-06-26 15:12:03

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score 64 · Answer 10 · 2024-02-18 04:08:38

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48

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34

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162

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score 143 · Answer 14 · 2022-10-28 02:07:03

143

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How to take the square root of a dual number ($\sqrt{a + b \cdot \varepsilon}$ with $a, ~b \in \mathbb{R}$ and $\varepsilon^{2} = 0$)?

Published on 28 Oct 2022 - 2:07

List Question

How to calculate $\arcsin$ of dual number: $\arcsin\left( x+y\cdot\varepsilon\right)$ where $x,y\in\mathbb{R}$ and $\varepsilon\ne0=\varepsilon^{2}$?

Function to approximate infinite series $\sum_{n=0}^\infty (-1)^n \frac{x^{2n}}{(2n+1)!}$

Possibility of computing antiderivative using dual numbers

Have generalisations of dual numbers/complex numbers/quaternions/octonions... been studied?

Is there a nice way to consistently define division by infinitesimals in the dual numbers?

What is $\zeta(\varepsilon)$ for Riemann's zeta function $\zeta$ and Dual Numbers' $\varepsilon$?

Raising a dual quaternion to a real number power

How is it possible that time can be represented as abstract element?

Closest rigid-body pose and velocity along a screw motion to a given pose

L'Hopital's rule with dual numbers

Imagining an exponential "hypercomplex" system

What's the definition of dual number at perspect of exterior algebra?

Matrix function derivative. Introduction

How to take the square root of a dual number ($\sqrt{a + b \cdot \varepsilon}$ with $a, ~b \in \mathbb{R}$ and $\varepsilon^{2} = 0$)?

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