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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Mellin transform of theta function $\theta$ to show $\zeta(-1)=-\frac{1}{12}$
Edit: I realize a lot of attention is pointed at the proclamation $\zeta(-1)=-\frac{1}{12}$. Im more interested in the derivation of the Zeta function using the methods describe below, thank you!
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How to find eigenvalues of a linear operator consists of laplacian?
I have the following matrix of linear operator consists of Laplacian \begin{bmatrix}0&1&0\\\Delta&\Delta& 0\\0&0&\Delta\end{bmatrix}
acting on \begin{bmatrix}w\\w_t\\u\end{...
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Find a unit vector from angles it makes with two other vectors
Suppose I have two vectors, $\textbf{x}_1$ and $\textbf{x}_2$; How do I find a unit vector, $\textbf{u}$, that makes angles $\theta_1$ and $\theta_2$ respectively with the originally mentioned vectors,...
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Is it easy to prove that for any $n$, $f^k(n)= 4$ for some $k$ or $f^k(n)= 1$ for some $k$ holds? (Mathematica book by Roozbeh Hazrat)
I am reading "Mathematica: A Problem-Centered Approach Second Edition" by Roozbeh Hazrat.
The following problem is Problem 8.13 on p. 137:
A happy number is a number such that if one ...
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I am stuck on the exercise with integral equation
It's exercise 23.10 from Mathmatical Methods for Physics and Engineering (Riley K.F., Hobson M.P., Bence S.J. 3d Edition).
Show that the equation
$$f(x) = x^{-1/3} + \lambda\int\limits_{0}^{\infty}f(...
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Sampling from intersection of sphere and simplex
I need to isotropically sample vectors in $\mathbb{R}^d$ of given Euclidean norm $C$ with a restriction that components are positive and add up to 1. Can someone suggest a method to do it?
I tried ...
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How to write integrals symbolically in Sagemath similar to Mathematica
In Mathematica you can input an integral symbolically by entering esc int esc. See the reference under the ...
- 101
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1
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How does Mathematica compute certain "bad" cases of the Meijer G function?
The Meijer G function $G^{m,n}_{p,q}\left(\begin{matrix}(a_1,\dots,a_p) \\ (b_1,\dots ,b_q)\end{matrix}\bigg|~z\right)$ is defined via a certain contour integral in the complex plane. In this ...
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Help with Runge-Kutta Order 4th with a system of 3 equations
I have been trying to solve a system of equations with Runge-Kutta Order 4th but every time I try to run the program it says running but it doesn't load anything so I can't check if it is good or not. ...
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Why do these solution graphs not match each other?
Consider the Initial Value Problem, $\frac{dP}{dt} = ((1 + f)^\frac{3}{5} (1 - f)^\frac{2}{5} - 1)P,\ P(0) = 100$, where $f$ is a real parameter between $0$ and $1$, inclusive. Its solution is $P = ...
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Having trouble with the integral of the second derivative of the function $e^{\frac{-1}{1 - x^2}}$ after a change of variables
The first thing I have to note is that I am not 100% sure whether this problem is due to Mathematica or just the mathematics I have produced. Thus feel free to direct me to the appropriate forum.
Let $...
- 1,030
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How do you apply the digit-extraction algorithm from Plouffe (2022)?
I recently became interested in programs that calculate pi, and I was reading about various spigot algorithms when I came across this Wolfram MathWorld site: https://mathworld.wolfram.com/Digit-...
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Why is this integration finite?
Consider $$\int_{2}^{2+\epsilon}\frac{1}{x^2-2^2}dx=\left.\frac{1}{4}\ln\left|\frac{x-2}{x+2}\right|\right|_2^{2+\epsilon}=\frac{1}{4}\left[\ln\left(\frac{\epsilon}{4+\epsilon}\right)-\lim\limits_{x\...
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Simplify and FullSimplify do not simplify a simple term
Why don't Simplify and FullSimplify work on: $\frac{\sqrt{a + \cos \theta}}{\sqrt{\frac{a + \cos \theta}{1 + a}}}$?
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Conversion of clockwise angle rotation to anticlockwise and vice versa
I have some data sets and using that data sets I'm trying to calculate the rotation numbers. Calculating rotation numbers I have to take some particular direction of vectors, i.e., either clockwise or ...
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