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.)

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Is Wolfram Alpha giving me a wrong answer?

I have asked for the convergence of the series $\sum (3^n/\sqrt{n})x^{2n+1}$, which has the radius of convergence of $1/\sqrt{3}$ and diverges at $|x|=1/\sqrt{3}$. However, the Wolfram Alpha is ...
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-1 votes
0 answers
26 views

Method of Maximum Likelihood Estimation

I have this continuous function $$f(x)=(ae^ax)/(e^ax+1)^2, \text{ for} -∞≤x≤∞. $$ And I got this log function I tried the following code in Mathematica n = Length[c]; logL = nLog[a] + Total[Log[...
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1 vote
1 answer
27 views

Hermite polynomials for non-integer degree

I have solved an eigenvalue problem using Mathematica and the answer is in terms of Hermite polynomials. Now, for integer degrees $H_n(z)$, I can find a nice definition. However, in the solution to ...
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3 votes
3 answers
156 views

Trying to duplicate in Mathematica a graph from Ordinary Differential Equations by Tenenbaum and Pollard

In the textbook Ordinary Differential Equations by Tenenbaum and Pollard they have a graph of this eqn: $x^3+y^3-3xy=0$ The graph is: I've tried: Plot[x^3 + y^3 - 3 xy = 0, {x, 0, 10}, {y, 0, 10}] ...
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-1 votes
0 answers
57 views

How do I write mathematica Wolfram language for this problem: Find the sum of all the multiples of 3 or 5 below 1000.

I am learning mathematica by doing. The answer is 233168. I got it by the following: multiple03= Range[333]*3 multiple05= Range[199]*5 Total[multiple03]= 166833 Total[multiple05]= 99500 Total[Range[66]...
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0 votes
0 answers
21 views

How to find evolution equation of certain geometric quantities under Ricci flow

I want to find evolution of certain geometric quantities, like Weighted Laplacian $\Delta_\phi:=\Delta-\nabla\phi\nabla$, where $\Delta$ is Laplacian operator and $\nabla$ is gradient operator, under ...
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1 vote
0 answers
30 views

Gaussian Integral like $\exp{[-r^2 - r_\alpha^2 +2 r r_\alpha \cos{(\theta-\theta_\alpha)}]}[r -r_\alpha \cos{(\theta-\theta_\alpha)}]f(r,\theta)$

I have a Gaussian kernel that I wish to evaluate $$\int_{0}^{\infty} \int_{0}^{2\pi} \exp{[-r^2 - r_\alpha^2 +2 r r_\alpha \cos{(\theta-\theta_\alpha)}]} [r -r_\alpha \cos{(\theta-\theta_\alpha)}]f(r,\...
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-3 votes
1 answer
64 views

Does this alternative way of calculating Twin Primes help to prove that there are an infinite number of Twin Primes?

I recently saw this video (https://www.youtube.com/watch?v=n4gmYjyI3vo) which explained a proof showing that all twin primes, when multiplied together, have a product where the digits of the product ...
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0 votes
0 answers
30 views

How is Mathematica minimizing correlation exactly with linear constraints?

I made a random data matrix as data = Table[Random[], {i, 5}, {j, 5}]; In my case it was $$ \left( \begin{array}{ccccc} 0.951203 & 0.546669 & 0.86928 &...
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0 answers
5 views

trying to add a line to my graph thats currently being manipulated in mathematica

Manipulate[ Plot[x^2 - 2 (m - 1) x + m (m - 3), {x, -30, 30}, PlotRange -> p], {m, -10, 10, 0.25, Appearance -> "Labeled"}, {p, -50, 1500, 50, Appearance -> "Labeled"}] I ...
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3 votes
1 answer
56 views

Cauchy's theorem and mathematica disagree? Integral involving branch points.

Consider the following integral: $$\int_{-\infty}^{\infty} \frac{dx}{\sqrt{x^2-2i\epsilon x -1}(x^2+1)}$$ where $\epsilon$ is an infinitesimal positive number. In the complex $x$-plane, the integrand ...
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0 votes
1 answer
96 views

How to solve this third order differential equation?

I need help to solve the following differential equation: $$A^{'''}y + A^{''}(-1 - y\cot{y}) - \frac{2A^{'}}{y} + \frac{2A}{y^{2}}(3+y\cot{y}) = 0$$ where $A$ is a function of $y$ and $A'$ represents ...
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1 vote
1 answer
39 views

Solving a differential equation with initial conditions only on the function

I have the initial value problem $\left\{\begin{gather}E_nf_n(x)+f_n''(x) = 0\\ f_n(-a)=f_n(a)=0 \end{gather}\right.$. Solving it using Laplace transform I get $$f_n(x) = f_0\cos(\sqrt{E_n}x)+\frac{...
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1 vote
0 answers
73 views

How do I plot 3D intersections of a system of inequalities using Matlab or Mathematica?

My question is inspired by the problem described here. Let us consider for example the following system of inequalities ($x,y,z\in\mathbb{R}$): $x+y+z>0$ $x^3+y^3+z^3<0$ $x^5+y^5+z^5>0$ How ...
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2 votes
0 answers
115 views

Problem with Legendre-Fourier series for sinx when the number of terms approaches infinity

After I learned about Fourier series expansion, I understand orthogonality of trigonometric functions was the key when I calculate the coefficients of Fourier series. As I knew that Legendre ...
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  • 21
0 votes
0 answers
25 views

An operation is defined on polynomials. How do I generalize it to other classes of functions?

I asked this question already here. Motivation part. I am currently researching divergent integrals. Definition. An extended number is an expression of the form $\int_a^b f(x)\,dx$, where $a,b\in \...
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  • 7,380
0 votes
2 answers
55 views

An explanation for the result of the following limit

Whilst having troubles in calculating the following limit, which I thought it were indeterminate, I decided to put it into W. Mathematica (the serious software, not W. Alpha online) and it returned ...
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1 vote
0 answers
55 views

Does the lognormal distribution satisfy the Fokker-Planck equation for geometric brownian motion?

I've been trying to understand the Fokker-Planck equation and have hit a road block on what is basically the second simplest possible example, geometric Brownian motion. Consider this Ito SDE for GBM, ...
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  • 346
0 votes
1 answer
48 views

To find a solution of non-linear PDE

Consider the following non-linear PDE: $u_x^2+u_y^2-u_{xx}-u_{yy}=2a+bz$ where $x,y,z$ are independent variables with $u=u(x,y)$ and $a,b$ are constants. I am trying to find at least one examples of $...
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  • 9,500
0 votes
0 answers
33 views

How to solve this boundless problem?

Try to make a function on $[0,1]$, which is unbounded in every neighborhood of every point.
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1 vote
0 answers
57 views

Derivation of an integral that generates a Bessel function of the second kind

I am working with a function where I need to solve an integral of the following form: where $K$ is a modified Bessel function of the second kind. The image is from "Integrals and Series: Volume ...
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0 votes
0 answers
56 views

How to find a solution to this differential equation?

I have the following differential equation: (1)$$ay''(x)+(b\cot(x)+c\sin(x))y'(x)+(c\cos(x)-b\csc^2(x)+\lambda)y(x)=0$$ of which Mathematica does not yield a solution, but it happens to be a slight ...
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1 vote
1 answer
68 views

Solving inequality, but graphing/mathematica gives a completely different answer

I have the following inequality problem, where I'm trying to solve for $\mu$. Here is the inequality: $$\frac{1}{2} \left(-\sqrt{(c+d+\theta -\mu +1)^2+4 (c \theta -\theta \mu )}+c+d+\theta -\mu +1\...
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  • 21
0 votes
0 answers
20 views

Mathematica package for computing Macdonald polynomials

0 I want to implement computation of Macdonald polynomials in mathematica. A similar question was raised in another question 5 years ago (Macdonald-Koornwinder polynomials?), but received no clear ...
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  • 433
0 votes
1 answer
38 views

Is my intuition of line integral or curl wrong?

My impression was that the curl of a vector field measures how fast a vector field turns along a closed curve around that point. Consider the vector fields $\vec{V}_1=-y\hat{i}+x\hat{j}$ and $\vec{V}...
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1 vote
1 answer
98 views

Understanding the Graph of a Multinomial Distribution

I am trying to understand exactly what information the graph of a multinomial distribution is supposed to convey. The thing I find strange is that a binomial distribution is graphed in two dimensions ...
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  • 1,654
1 vote
0 answers
38 views

How to solve simple 2D space-time PDE numerically

I have a 2D space-time PDE and I want to solve it numerically over the time axis. The time initial field is already known with respect to space, i.e., the spatial distribution is already known at time ...
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0 votes
2 answers
161 views

Graphing parametric equation software? Desmos/Mathematica/ other math software?

I want to view what the graph of, for example, $x=\sin t,\quad y = \sin(10t)$ looks like, but not as a static graph $\ y=f(x),\ $ but rather one where we can see the movement of the point on the $\ x-...
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1 vote
0 answers
47 views

Conditions on the coefficients that the roots of a polynomial be less that or equal to unity in absolute value

Consider the polynomial $$f(x)=p_0x^n+p_1x^{n-1}+...+p_{n-1}x+p_n,~p_i \in \mathbb C.$$ Particularly, in the case of absolute stability of a multi-step numerical method, how can we find out the ...
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4 votes
0 answers
118 views

How Can I Visualize a PDE Boundary Condition?

In this question, the comment suggests that the integration bounds in the Fourier Series should be chosen to avoid discontinuities in the boundary conditions. I am trying to produce a nice visual to ...
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  • 1,654
0 votes
0 answers
47 views

What algorithm does mathematica use to compute the Gauss hypergeometric function?

I recently tried implementing Gauss Hypergeometric function with c++ in two different ways, but found that they each had some problems in certain parameter regions. The first way uses the naive series ...
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7 votes
0 answers
266 views

A generalization of Elon Musk's favorite interview question (Going 1km South, 1km West, then 1km North returns to the starting position).

This question concerns a generalization of the following problem (allegedly, in the early days of Tesla and SpaceX, Elon Musk would ask the following question to possible future employees): Assume ...
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1 vote
0 answers
66 views

Is it possible to solve this inequality?

I need to solve this inequality for $j$ and I am having a hard time. I also tried to use Mathematica but it did not work. Do you have any idea of how to proceed? Any tips on the procedure is very ...
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0 votes
0 answers
41 views

Hypergeometric function and testing

We have the following term $$F(x):= \sum_{d= 1}^\infty \sum_{k=1}^d (-1)^{d-k}\frac{1}{d! h^d} \binom{d-1}{k-1} \, \prod_{i=1}^d G((k-i)h) \, x^{d} \tag{*} $$ where $G(z)$ is a rational fixed function....
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1 vote
0 answers
37 views

Mathematica Kampé de Fériet Notation

I'm looking at the definition of the Kampé de Fériet function in Mathematica's Notation Reference Document (p.36 here), and there is one part of their notation that I'm not quite sure about. In the ...
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0 votes
2 answers
47 views

How to find the coefficent of a term in a Dirichlet generating function in Mathematica?

For a normal Dirichlet generating function like $Zeta[s]^2$, I can get the coefficient of the n-th term by applying Dirichlet convolution of the two constant functions. But how to find the coefficient ...
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  • 243
1 vote
1 answer
79 views

Mathematica's evaluation of nested summations

Suppose we want to count the number of instructions executed by the following Python code: ...
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  • 235
0 votes
4 answers
83 views

Evaluating $\lim_{z\to n}\frac{\Gamma (1-z)}{\Gamma (1-2 z)}$ using Mathematica

I am trying to evaluate: $$\lim_{z\to n}\frac{\Gamma (1-z)}{\Gamma (1-2 z)}$$ Here are my steps: \begin{align*} \lim_{z\to n}\frac{\Gamma (1-z)}{\Gamma (1-2 z)}&=\lim_{z\to n}\frac{\Gamma (-n-z+1) ...
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1 vote
1 answer
167 views

Why is $\lim\limits_{x\to\infty}\frac{\sum_{i=1}^x(\sum_{j=1}^i\frac1j-\ln i-\gamma)}{\sum_{i=1}^x\frac1i}=\frac12$?

$$ \mbox{Why is}\quad\lim_{x\to\infty} \frac{\sum_{i = 1}^{x}\left[\sum_{j = 1}^{i}1/j -\ln\left(i\right)-\gamma\right]}{\sum_{i = 1}^{x}1/i} = \frac{1}{2}\ ?.$$ I learnt Euler's Constant $\gamma$ ...
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0 votes
0 answers
47 views

Finding the derivative for this seemingly complicated function

I have the following equation - $$I = \exp\left(\int_{t_0}^{t}\frac{-B-A|u(t)|^2}{AB}\ \mathrm{d}t_1\right)\cdot\left(1 + \int_{t_0}^{t}\frac{\exp\left(-\displaystyle\int_{t_0}^{t}\frac{-B-A|u(t)|^2}{...
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  • 329
2 votes
0 answers
48 views

Classifying and Efficiently Generating Graphs for Juggling Patterns

Short Version: Is there a way to uniquely specify the set of graphs that can represent juggling patterns of length $n$ (or of any length less than $n$, if that's easier)? A necessary condition (but ...
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0 votes
0 answers
62 views

Finding Roots of a Polynomial in a Given Range

I want to be able to analyze complicated polynomials (degree $6,7$ etc.) and find out if they have roots in a given range. How do I proceed to do this using Mathematica, Matlab, or analytically(if ...
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0 votes
0 answers
24 views

NIntegrate of a function defined by NIntegrate in Mathematica

Suppose you have to solve the following problem: h[s_]:=NIntegrate[1/g[x],{x,0,s}] And: H=NIntegrate[h[q],{q,0,1}]; Mathematica returns the following error: NIntegrate::nlim: x = q is not a valid ...
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1 vote
0 answers
22 views

Differential quotient for a function in 0

To show that a certain function is differentiable in $L=0$ i tried to calculate the differential quotient for $L\to 0$ $$\frac{1}{L} \cdot \left( \left(\frac{k-\sqrt{k^2+i\frac{\kappa}{L}}\frac{\left( ...
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  • 203
2 votes
1 answer
103 views

Madelung Constant

I have been working in this series $$\sum _{m=0}^{\infty } \sum _{k=0}^{\infty } \sum _{j=0}^{\infty } \frac{(-1)^{j+k+m} \left((j+1)^2+(k+1)^2+(m+1)^2\right)}{\left((j+1)^2+(k+1)^2+(m+1)^2\right)^{3/...
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3 votes
2 answers
99 views

Computation of irreducible characters for $S_n$ - Mathematica vs. GAP

For some physical applications I need the knowledge of irreducible characters for symmetric groups $S_n$ with large $n$. For small ones I was using FiniteGroupData ...
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  • 2,920
0 votes
1 answer
45 views

Numerical integration of an integral with singularity

I am trying to solve this integral numerically using Mathematica. Here is my integral $$\int_0^{\infty} dx\;\frac{\Gamma(\delta-4ix)}{(i(x-1)+\epsilon)^{1-4ix}}\;, $$ where $0<\delta,\ll 1$ and $0&...
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1 vote
3 answers
132 views

Integrating $\int_0^\infty \frac{x^n}{e^x+1} \,dx$, where $n$ is an integer

If the general case is too hard for some reason, I mostly need the $n=2$ case of the following integral: $$ \int_0^\infty \frac{x^n}{e^x+1} \,dx $$ For some reason Mathematica fails me, as it claims ...
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1 vote
0 answers
55 views

Subgraphs with diameter 2

When examining the modularity of graphs or networks, concepts like "blocks", "clusters", or "communities" are used, more or less strictly defined as (maximal) subgraphs ...
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1 vote
1 answer
52 views

Continuation of Hypergeometric Function when $a - b$ is natural number

I am currently implementing the 2F1 Gaussian hypergeometric function numerically, and need to know its continuation for $ |z| > 1 $. I have researched this and found this nice formula in the ...
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