# 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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### 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[...
1 vote
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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
1 vote
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### 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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### 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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### 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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### 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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### 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 ...
1 vote
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### 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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### 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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### 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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### 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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### 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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### 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) ...
1 vote
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### 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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### 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 ...