Questions tagged [mathematica]

Question 1

I work on the following equation $$ \frac{1}{z_1+z_3} = \frac{1}{z_1+z_2} + \frac{1}{z_1} + \frac{z_1}{z_2} + \frac{1}{(z_1+z_2)^2}. $$ Let $z_1$ and $z_2$ be given by $z_1=\frac{1}{2}\exp(i\alpha)$ ...

Question 2

Define the sequence of functions $a_n$ such that $a_0 = f(x)$ and $a_n = \int a_{n-1}dx$ if $n \geq 1$ and $f(x)$ is an analytic function. Then $\lim_{x \to 0}a_n = -C_n(g(1/x))$ for all $n \geq 0$ if ...

Question 3

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 $\alpha$, but now I assume I’m incorrect. Here is ...

Question 4

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\...

Question 5

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 ...

Question 6

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 ...

Question 7

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}}{...

Question 8

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 $n>p>0$, $n,p\in\mathbb{N}$. I have ...

Question 9

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....

Question 10

The result of $$\int_0^1 \frac{\ln(x+a)}{x^2+1}\, \mathrm{d}x$$ should be real for positive number $a$, but Mathematica always gives a result full of terms like $$\mathrm{i} \cdot \operatorname{...

Question 11

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 "...

Question 12

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 ...

Question 13

Simple question, I’ve the following type of equation to solve in order to build the inputs parameters for an algorithm : ...

Question 14

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 ...

Question 15

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 ...

Stack Exchange Network

Questions tagged [mathematica]

Finding specific points on a complex parametric curve [closed]

Why does $\lim_{x \to 0}a_n = -C_n(g(1/x))$?

What is the Hausdorff dimension of this Cantor-like set?

ROC for $\mathcal{L}_s[a^x]$ for $a \in \mathbb{R}$ && $a>0$

Complex Integral Evaluation with complex conjugates and absolute values

Computing the real root of $\frac{(1-n)^{n-1}}{n^n}x^n+x-1 = 0$ analytically

Justifying a closed-form integral derived by Mathematica

Trigonometric integral problems related to hypergeometric function

Get different geographical distances on earth (modeled as ellipsoid)

Is there any "nice" form of $\int_0^1 \frac{\ln(x+a)}{x^2+1} \mathrm{d}x$ ($a>0$)?

Help visualise this problem from a math olympiad

Findng a closed form expression for axially symmetric solutions in spherical coordinates with known infinite series Legendre polynomials

In terms of performance, how to get a solution to this mathematica equation having large constants with y×67 being a perfect square?

Define a function as the nth derivative of an infinitely differentiable function of n for all real numbers

Calculating Jones polynomials for virtual links in mathematica

Hot Network Questions