Questions tagged [mathematica]
For questions concerning the popular computational software program published by Wolfram Research. (Note: you are more likely to get quicker and more accurate response if you ask the question on their user forum or on the Mathematica Stack Exchange site.)
732 questions
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Levinson Recursion With Sub-Singular Hermitian Toeplitz Matrices Fails for Complex Inputs [closed]
I’m trying to implement the Levinson recursion for Hermitian Toeplitz systems, including cases where some leading principal minors are (nearly) singular. The implementation works for real-valued ...
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What is the Hausdorff dimension of this Cantor-like set?
Suppose $\alpha=\ln(2)/\ln(3)$. (This is the Hausdorff dimension of the Cantor set.) I originally assumed the Cantor-like set has Hausdorff dimension $\alpha,ドル but now I assume I’m incorrect.
Here is ...
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ROC for $\mathcal{L}_s[a^x]$ for $a \in \mathbb{R}$ && $a>0$
Question: What is the ROC (region of convergence) for the laplace Transform $\mathcal{L}_s[a^x]$ for $a \in \mathbb{R}$ && $a>0$
My attempt:
$$\begin{align}
\mathcal{L}_s[a^x] &= \int\...
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1
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Complex Integral Evaluation with complex conjugates and absolute values
I need some help solving this integral here. I am trying to run a code in Mathematica, but the running time is awfully long. Does anyone have any tips/tricks on how to do it faster? Any help is ...
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Computing the real root of $\frac{(1-n)^{n-1}}{n^n}x^n+x-1 = 0$ analytically
I have the following trinomial equation
$$
\frac{(1-n)^{n-1}}{n^n}x^n+x-1 = 0,
$$
where $n=1-\frac{1}{m}$ and $m > 1$. I want to compute the single root of this equation by evaluating the ...
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2
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Justifying a closed-form integral derived by Mathematica
I was intrigued by this previously bountied question, which investigates the integral
$$\int_{0}^{+\infty}\left[\frac{1}{\sqrt{1-e^{-t}}}\exp\left(\frac{2xye^{-\frac{t}{2}}-\left(x^2+y^2\right)e^{-t}}{...
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Trigonometric integral problems related to hypergeometric function
I am dealing with two integrals:
$$
\int \frac{\cos[(n+\frac{1}{2})x]}{\sin^{p+1/2}x}dx,\qquad
\int \frac{\sin[(n+\frac{1}{2})x]}{\sin^{p+1/2}x}dx
$$
where $n>p>0,ドル $n,p\in\mathbb{N}$. I have ...
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Get different geographical distances on earth (modeled as ellipsoid)
Using Vincenty's formulae with
$$P_{\text{Frankfurt}}=(50.11552, 8.68417)$$
$$P_{\text{Rio}}=(-22.9083, -43.1964)$$
and get the shortest geographical distance (World Geodetic System)
$$s\approx 9564....
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Is there any "nice" form of $\int_0^1 \frac{\ln(x+a)}{x^2+1} \mathrm{d}x$ ($a>0$)?
The result of $$\int_0^1 \frac{\ln(x+a)}{x^2+1},円 \mathrm{d}x$$ should be real for positive number $a,ドル but Mathematica always gives a result full of terms like $$\mathrm{i}
\cdot \operatorname{...
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Help visualise this problem from a math olympiad
My teacher told me to explain how I solved that problem to the class and I did, but some people can't understand the logic of adding the vectors and the rotations. Would it be possible for the "...
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64
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Findng a closed form expression for axially symmetric solutions in spherical coordinates with known infinite series Legendre polynomials
I have two infinite series of axially symmetric solutions in spherical coordinates $(r, \theta)$ , one series is expanded using the Legendre polynomials $ P_n (\cos\theta)$ , and the other series is ...
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190
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In terms of performance, how to get a solution to this mathematica equation having large constants with y×67 being a perfect square?
Simple question, I’ve the following type of equation to solve in order to build the inputs parameters for an algorithm :
...
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Define a function as the nth derivative of an infinitely differentiable function of n for all real numbers
Can we define a function $\alpha$ which is the $n^{th}$ derivative of some infinitely differentiable function $f(n)$ for all real $n$? That is, $\alpha(n) = \frac{d^n}{dn^n} (f(n)) = f^n(n)$. This ...
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Calculating Jones polynomials for virtual links in mathematica
So, the KnotTheory package for Mathematica is advertised as working for classical links. But one can construct a PD code for a virtual link as well. Will this package correctly calculate the Jones ...
2
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1
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150
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Solution of coupled trigonometric equations
I am trying to solve these equations, where $k$ is a real-valued parameter:
\begin{align}
&\cos{x} + k(\sin {x} - \sin(x+y) - 2\sin y ) - \cos( x+y) = 0, \nonumber\\
&\cos{y} + k(2\sin ...