# Tagged Questions

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### Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
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### Approximate analytic solution to a polynomial equation

The analytic solution of the equation $$1-\frac{2M}{r}+\frac{Q^2}{r^2}-\frac{\Lambda}{3}r^2 = 0$$ obtained by using the code ...
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### Why does MiniMaxApproximation fail in this simple case?

Why does MiniMaxApproximation[Erfc[t], {t, {0, 2}, 0, 1}] give the following error? ...
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### Looking for a convenient way to replace a large data sample with an analytic approximation

Suppose that data is a large data sample, and that Histogram[data] produces a very smooth-looking distribution. Since ...
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### How does WolframAlpha calculate closed form approximations of irrational numbers? [closed]

How does WolframAlpha do this: I'm aware of services such as RIES, which is an inverse equation solver, and ISC, the Inverse Symbolic Calculator. But WA goes much further. I've tried doing a ...
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### Approximation of $f(x)$ at large values of $x$?

Suppose you a function $f(x)=1/x+x^2$. At large values of $x$, it is closely approximated by $f(x)=x^2$. Can Mathematica do this for me for a more complicated function? How would I input the ...
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### Efficient Lloyd Sampling of Images

I want to sample a grayscale image so that every voronoi cell contains approximately the same total intensity using lloyd sampling. My current code is kind of slow and I was hoping for some advice to ...
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### Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
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### How do I estimate the Pareto front in my multiobjective optimization problem?

I need to minimize a function of two parameters that gives two "stress" outputs {A,B} = f[tau,mu]. How do I estimate (even roughly), the Pareto front for this ...
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### Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
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### Trying to find the best Padé approximant for a given number of terms

Let suppose that I have a function $f[x]$ I want to approximate using a PadÃ© expansion and that I decide what would be maximum number of terms to be used. Is there any way with Mathematica to find ...
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### How can I get an approximate contour plot from a 3D plot?

I have some larger square, Hermitian matrices, M, (dimension 20, say, much more than 4) with 2 independent variables, call them x and y. I can plot the eigenvalues as functions of x and y with: <...
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### Assigning an analytical approximation to the error function erf(x)

Working with some iterative integral equations, I have Gaussian density functions involved therein. Integrating the Gaussian function I obtain the error function. When I take the second integration, ...
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### Compute coefficient of Generating function

Given a generating function $F(z)$, is there any way to compute the coefficient $a_k$ of $z^k$ by Mathematica? One method is to calculate by the equation $\frac{F^{(k)}(0)}{k!}$. However, this ...
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### How to improve the accuracy of this Monte Carlo simulation

A friend of mine went on an interview and he was asked to calculate the angle between the hour hand and minute hand of an analog clock when the time was 3:15. Arguably, this is a trivial problem that ...
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### Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: \$a_1(1+4\alpha_2)^3+8a_2(1+4\alpha_1)^2+\frac{\sqrt{\pi}}{64}(1+4\...
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### How to visualise an iterative approximation to pi

I'm experimenting with different algorithms that approximate pi via iteration and comparing the result to pi. I want to both visualise and perhaps know the function (if any) that describes the ...
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### Decimal representations of analytic values in an expansion

I have a solution to an ODE (which I call sol), which I would like to expand in terms of Log[1+x] around x=-1. I thought that: ...