# Questions tagged [approximation]

For questions that involve concrete approximations, such as finding an approximate value of a number with some precision. For questions that belong to the mathematical area of Approximation Theory, use (approximation-theory).

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### Approximating probabilistic event by Central Limit Theorem

We're throwing a die 3600 times. Let $X_i$ be the number rolled, and $S_n=X_1+...+X_n$. By the law of large numbers, we know $\mu_Χ=3.5$. We want to approximate the probability that $\frac{S_n}{n}$ ...
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### Chebyshev approximation for bivariate function

I read the paper. I am a litte bit confused regarding formulation of Chebyshev approximation for bivariate function(See photo). There is only one integral over variable x. Should it be in formula one ...
1 vote
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### Proof of transformation of Hypergeometric to Whittaker.

I am working on this paper, regarding the spectrum of a certain operator in the hyperbolic plane, and at a certain point are presented with an hypergeometric function \begin{equation} \text{}_2 F_1\...
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### Approximation of the n'th prime

An old paper by Ernest Cesàro provides a suggested approximation of the n'th prime. The expression and the reference currently appears in the Wikipedia article on the Prime Number Theorem. It is ...
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### Compute $\int_0^{0,2}\frac{1-e^{-x}}{x}dx$ accurate to $\alpha=0,0001$

$\int_0^{0,2}\frac{1-e^{-x}}{x}dx$ I was trying to compute integral,cause it'll look like alternative series. I'm stuck and have troubles to calculate this integral. in first task,that looked like ...
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### Best approximation of a line by a rational line [closed]

Let n be a positive integer and let $Q_n$ denote the set of rational numbers whose denominator is bounded above by n. Given an arbitrary line L: $Ax+By = C$, with $A,B,C \in \mathbb{R}$ I want to find ...
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### Help to improve polynomial approximation with example of sine approximation

I found that composition of polynomials has interesting properties for approximation. (1e-20 error for 6 coefficients). In pseudocode $\ p2=x+ax^3+bx^5$ ...
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### Multiplicative Harmonic Series

Is there any approximation formula for this equation? I have been trying to find approximations for it so I can create an approximation formula myself for something else, but for some reason I can't ...
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### Integrable approximation of error function over Gaussian measure

I am interested in a problem that involves computing the expectation of of the CDF $\Phi$ (or equivalently erfc shifted and scaled) for the standard normal distribution, for $x$ normal distributed ...
1 vote
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### Approximating for the Error function $\text{erf}(x)$ through an Hyperbolic tangent function $\text{tanh}\left(\dfrac{4x}{4-x^2}\right)$

Approximating for the Error function $\text{erf}(x)$ through an Hyperbolic tangent function $\text{tanh}\left(\dfrac{4x}{4-x^2}\right)$ I was plotting some functions and I found that the function f(...
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### Help understand this solution/Approximation

Good day everyone. In this appendix, particularly this part, the author approximated $1-aR$ with $e^h$ where $h=2.5$. Can anyone explain to me how did the author get this outcome? Variable $a$ is a ...
1 vote
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### Approximation of a Generalized Hypergeometric Function

Is there any approximation with an "elementary function" for the following generalized hypergeometric function, especially for very large values of $n$ and $0 < p < 1$? I mean, without ...
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### How is the Chebyshev polynomial approximation defined when using the spectral method to numerically solve PDEs?

I am studying spectral methods for numerical solutions for PDEs. Currently, I am on a chapter that explains how to use Chebyshev polynomials to solve non-periodic boundary value problems. I understand ...
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Given that ...
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### Linear approximation using $2D$ Linear Interpolation

Probably it is a simple question. but even after several hours of research, I could not find anything relevant. I have a function $f(x,y) = xy$, with $x$ and $y$ that belong to bounded, continuous ...
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### Efficient and Accurate Formulas for Approximating sin x , cos x , tan x and ln x.

Summary: I am currently studying various mathematical functions and their real-world applications. I'm particularly interested in trigonometric functions $( \sin, \cos, \tan )$ and the natural ...