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.)
722
questions
1
vote
0
answers
33
views
Sum with constraints in maple or mathematica [closed]
I'm looking for a code in Maple or Mathematica to evaluate and give a list of terms in expressions like
$\newcommand{\on}[1]{\operatorname{#1}}$
$$
\sum_{a\ +\ b\ +\ c\ =\ 6}\on{f}\left(a\right)\on{f}\...
- 13
0
votes
1
answer
60
views
How to visualize triangle using a software
How to visualize (using some plotting software) the triangle inequality, $|x-z|\le|x-y|+|y-z|$, where $x,y$ and $z$ belong to some finite intervals.
I am asking for general way, for example, $(x-z)^2\...
- 375
-2
votes
0
answers
52
views
Numerically solved PDE of Ornstein–Uhlenbeck process on 2-Simplex violates conservation of probability [closed]
Thanks for your consideration.
I'm working to create a solution of an Ornstein-Uhlenbeck process with a force that takes mass towards the centre of a Simplex. I'm assuming absorbing boundaries.
The ...
- 15
0
votes
0
answers
20
views
Extracting coefficients from falling factorial form in Mathematica
I have a polynomial in falling factorial form, i. e.
$-x+7(-1+x)x+6(-2+x)(-1+x)x+(-3+x)(-2+x)(-1+x)x$.
Now i want to extract the "outermost" coefficients $\{-1,7,6,1\}$. I have this code to ...
- 141
1
vote
1
answer
54
views
Logarithmic Function Calculation in Mathematica
I find these results in the evaluation of the logarithms that only differ in the sign $-$ I do not understand why in the first case $\operatorname{Log}[x+1]/8$ is not returned as an answer.
6
votes
2
answers
95
views
Optimal length of rope for sliding across a gap
I'm trying to solve a physics problem that I heard ~10 years ago in undergrad that was casually posed to me without a solution in mind; it has been bothering me ever since! Please let me know if this ...
- 262
4
votes
0
answers
144
views
Analysis of a sequence based on ratios of floors of consecutive powers of a real value
I am currently interested in the following sequence:
Fix a number $x$, and define a sequence $(a_n)_{n=0}^\infty = \lfloor x^n \rfloor$ and $(b_n)_{n=0}^\infty = \frac{a_{n+1}}{a_n}$
With a little ...
- 411
0
votes
0
answers
22
views
Definite Integral involving polynomial and Meijer G-function
I am trying to solve the following integral involving Meijer-g function
$\int_0^{\infty} \left(\varrho x + \nu\right)^{p+\frac{1}{2}-\frac{k}{2}} G_{1,3}^{3,0}\left(\begin{matrix} \frac{\...
- 31
1
vote
1
answer
95
views
Fourier transform of incomplete gamma function
Ultimately I am interested in the Fourier transform of
$$
e^{-i\zeta}(-i\zeta)^{-2\epsilon}\Gamma(2\epsilon,-i\zeta)
$$
in a series expansion around $\epsilon=0$, so to first order in
$$
\lim_{\...
- 133
0
votes
0
answers
26
views
Uniform initial conditions make Fokker-Planck/Kolmogorov Equation boundary conditions inconsistent
When considering the time evolution of a distribution over a state variable $x$, one of the cases that seems fundamental is when knowledge about $x$ begins uniform. However, modelling the process as ...
- 15
0
votes
0
answers
74
views
Software packages to compute finite type invariants of Polygonal Knots
Assume I have a polygonal knot, $K$, represented as its set of vertices $\{\mathbb{v}_i| \mathbb{v}_i\in\mathbb{R}^3\}_{i=1,...,n+1}$, where $n$ is significant, let's say $100<n<500$.
Which ...
- 51
0
votes
0
answers
52
views
Difficulty in computing integral
I am currently struggling with computing the following integral (as a whole). First, I define the following function.
\begin{equation}
f(q) = \frac{840q + 190 q^3 + 93 q^5 - 15\sqrt{4+q^2}(28+4q^2 + ...
- 257
0
votes
0
answers
25
views
Solving Diophantine Equation in Macaulay2
I have to write a function which solves the diophantine equation $p(s)x^2 = q(s)$ (in $x$) where $p,q$ are integers polynomials in $s.$ This is doable since $p(s) \mid q(s)$ has only finite solutions (...
2
votes
1
answer
67
views
Reduce $\frac{d^{n-1}}{dw^{n-1}}\frac{4^{-n/{\sqrt w}}}{\sqrt w}\Big|_1=\frac1{\sqrt\pi}G^{3,0}_{1,3}\left(^{3/2-n}_{0,1/2,1/2};(\ln(2)n)^2\right)$
In this
answer to Is there any valid complex or just real solution to $\sin(x)^{\cos(x)} = 2$?,
one must calculate $$\frac{d^{n-1}}{dw^{n-1}}\left.\frac{4^{-\frac{n}{\sqrt w}}}{\sqrt w}\right|_1=\...
- 12.5k
0
votes
1
answer
81
views
Simulation of a pendulum on a spinning Disk
I don't know if this is the right place to ask this Question, but I have previously asked a similar question where i asked how to write a simulation on this phenomenon. I got a great answer with a ...
- 119
0
votes
0
answers
35
views
Need help in implementing q-SeriesToq-Product in Mathematica
In Mathematica Guidebook for symbolic computations (https://www.amazon.com/dp/0387950206/wolframresearch-20), in the Exercises, 30 (c)(p. 359), there is a question:
I have no clue how to implement ...
- 21
0
votes
0
answers
41
views
A question regarding asymptotics in mathematica
I am trying to see the asymptotics of the Var function as below, from the plot it seems it goes to $-\infty$, however, I also calculate its asymptotics which gives me a positive $+\infty$.. Why could ...
- 1,052
0
votes
0
answers
49
views
Mathematica PDE solving
I'm new to Mathematica and have never solved a PDE before. I tried to follow a textbook to get equation 4, but got something different with Mathematica (I got $(4\pi Dt)^{1/2}$ instead of $(4\pi Dt)^{...
- 169
0
votes
0
answers
32
views
Checking Positivity
enter image description here
I am trying to check positivity of an algebraic expressions where all the variables are positive. Using Mathematica 9.1 version I have got the result showed as follows. ...
- 11
2
votes
1
answer
111
views
Asymptotic analysis for integrals
I am a physics student doing some integrals of the form
$$\lim_{\rho\to\infty} \int dx \int dy \text{ }f(x,y) e^{-\rho (x y)^{3/2}}$$ with $x,y \geq 0$, and $f(x,y)$ is a polynomial ($a_0+a_{x1} x + ...
- 23
0
votes
0
answers
29
views
Weighted sum of specific multinomial coefficients
Let $A$ and $b$ be nonnegative integers and consider the sums
$$\sum\limits_{c=0}^{b/2}\frac{1}{4^c}\binom{A}{c,b-2c,A-b+c}$$
and
$$\sum\limits_{c=0}^{b/2}\frac{c}{4^c}\binom{A}{c,b-2c,A-b+c}.$$
I ...
- 1,147
1
vote
1
answer
64
views
Algorithm and program for modelling a Free Nilpotent Lie algeabra
I need to compute in a Free Nilpotent Lie Algebra $L$ given by a finite list of generators. For example, put the generators $\{A, B\}$. So, the linear generators for the space of $L$ is
$$\{A, B, [A,B]...
- 21
1
vote
0
answers
42
views
How to define a linear operator in Maple that commutes with derivatives?
I would like to simplify an expression involving the Hilbert transform in Maple. The Hilbert transform is defined by $$ Hf(x) = \frac{1}{\pi} \ \mathrm{p.v.} \int_{-\infty}^{+\infty} \frac{f(z)}{z-x} \...
- 11
-4
votes
1
answer
68
views
Can you help me to solve this PDE? [closed]
Could you please help me to solve the following equation?
\begin{equation}
u_{yyyy}+u_{xy}-a\,\left(u\,u_y\right)_y\,=\,0
\end{equation}
Where
\begin{equation}
u\,=\phi^{\alpha} \sum_{k\,=\,0}^{\...
- 1
1
vote
0
answers
93
views
The inertia degree of a field over the decomposition field
$K/F$ is a Galois extension of algebraic number field, $\mathfrak{p}_{i}$ are prime ideals of $K$, and $\mathfrak{p}= \mathfrak{p}_{1}$.
Decompose a prime ideal $\mathcal{p}$ of $F$ in $K$.
$$p(=po_K)=...
- 94
1
vote
0
answers
41
views
regularized incomplete beta function integration
Solve $\int_{0}^{1}\frac{I_{u^{\frac{1}{p}}}\left ( p+\frac{1}{a} ,1-\frac{1}{a}\right )}{u}du$ . In Mathematica, this integral does not converge but from an article, I got the answer to this integral ...
1
vote
1
answer
81
views
Finding the eigenvectors for a $2\times 2$ matrix
Some lecture notes I’m reading present the following matrix:
\begin{equation*}
L =
\begin{pmatrix}
0 & a \\
b & c\\
\end{pmatrix}
\end{equation*}
It then says that the dominant eigenvalue $ \...
- 163
-1
votes
1
answer
62
views
minimal polynomial of a complex number in Mathematica [closed]
How do I calculate the minimal polynomial of $a+ \mathcal{i} b$ where $a,b \in \mathcal{R}$ in Mathematica. In Mathematica, if I give specific values of a and b, then it gives the solution, for ...
- 73
1
vote
1
answer
314
views
Difference in differentiation between Mathematica and Wolfram Alpha
I am trying to differentiate this:
$$f(x)=e^{-x^2}$$
In Wolfram Alpha I get this:
$$-2x\,e^{-x^2}$$
But in Mathematica I get:
$$-2x\,e^{-x^2}\log(e)$$
Why the difference?
- 341
2
votes
1
answer
131
views
Why does CubeRoot and power of 1/3 give different answers in Mathematica?
I have these 2 functions, which should give identical answers:
GPrime[x_] := (1/CubeRoot[x]) + 1
GPrime2[x_] := (1/(x^(1/3))) + 1
However, given this:
...
- 341
0
votes
0
answers
22
views
Radial wavefunction at origin for excited states $|{R_{nl}}^2| (0)$ for quarkonium
I am solving the radial Schrodinger wave equation for quarkonium containing a quark and antiquark. The system is non-relativistic as quarks are charm and bottom which are heavy. The wave equation is ...
- 1
12
votes
2
answers
252
views
Does $\frac{1}{1-e^{-\frac{1}{e^x}}} - e^x - \frac{1}{2} $ really explode with oscillatory behavior past $x = 15$?
I was looking at the function
$$ \frac{1}{1-e^{-\frac{1}{e^x}}}-e^x - \frac{1}{2}$$
I thought I had reason to believe this tends to 0 as $x$ tends to positive infinity because
$$ \sum_{n=0}^{\infty} ...
- 17.5k
0
votes
2
answers
97
views
Mathematica help to check a positive definite matrix
I am new to Mathematica and am trying to check if the following matrix is positive definite with the program. The answer is supposed to be yes because $x > 0$ and $y > 0$ but I don't know how to ...
- 9
1
vote
1
answer
211
views
Solution to degenerate case of hypergeometric differential equation
I am trying to find two independent solutions of this differential equation: $$x(1-x)y''(x)+\left[\frac d2-\left(d+\frac12\right)x\right]y'(x)-\frac{(d-1)d}{4}y(x)=0,$$ for $0<x<1$.
This is a ...
- 171
0
votes
0
answers
71
views
Evaluating Function of Incomplete Elliptic Integrals
I am trying to write Mathematica code that evaluates the following function:
$$
f(\kappa_{yx}, \kappa_{zx}) = 1 + 3 \kappa_{yx} \kappa_{zx} \frac{E(\varphi \backslash \alpha) - F(\varphi \backslash \...
0
votes
1
answer
138
views
Partial Differential Equation on a Riemannian Manifold: How to solve complex second order ODE by hand.
I'm working on a project where I discuss using the metric tensor to compute the Laplacian on various Riemannian Manifolds, and how that can aid in solving certain Partial Differential Equations. In ...
0
votes
1
answer
58
views
Feeding parameters into a multivar function in Mathematica
I am trying to find an intersection point between a plane and a line. I defined my line as a function of $x,y$ and $z$.
g[x_, y_, z_] := 5 x - 8 y + 2 z - 13
I ...
- 15
0
votes
1
answer
51
views
Difference in expected values in Mathematica? [closed]
Could someone explain why I am getting different outputs when I calculate the following two expressions on Mathematica?
First:
...
- 1
0
votes
2
answers
195
views
what are the branch points and branches of $g(z)=(z+ \sqrt{z})^{1/3}$?
And what if we for example shifted one of the roots, eg $f(z)=(z+ \sqrt{z-3})^{1/3}$?
I already asked a more extensive version of this question here Branch cut/ points for square roots inside cubic ...
- 67
0
votes
0
answers
92
views
Branch cut/ points for square roots inside cubic roots- incorrect branching by mathematica or my mistake?
There's a lot of great information here about understanding the branch cuts and branch points of functions of the form ( for example ) $(z^3+1)^{1/2}$, sums of simple roots and products thereof.
...
- 67
1
vote
0
answers
85
views
Minimizing $\frac{1-c}{1-\frac{(a-b)^3}{(1-a)^2} - \frac{(b-c)^3}{(a-b)^2} - \frac{c^3}{b^2}}$
I am interested in approximating the minimum of
$$\dfrac{1-c}{1-\dfrac{(a-b)^3}{(1-a)^2} - \dfrac{(b-c)^3}{(a-b)^2} - \dfrac{c^3}{b^2}}$$
Subject to $0 < \frac{a-b}{1-a} < \frac{b-c}{a-b} < \...
- 2,457
2
votes
1
answer
97
views
Minimizing $\frac{1-\int_{1-\int_{0}^1 F(r)dr }^1 F(t) dt }{1-\int_{0}^1 F(t)^2 dt}$ for increasing function subject to $F(0)=0, F(1)=1$
Let $F:[0,1]\to [0,1]$ be an increasing function with $F(0)=0, F(1)=1$. Define $A(x)=1-\int_{x}^1 F(t) dt$. I am trying to approximately minimize the following ratio across all $F$ (i.e find a lower ...
- 2,457
1
vote
1
answer
60
views
Simplifying a particular expression
I have the expression
$$ \frac{x(-c z^{n+1} (-1)^k + c x^{n+1})}{(x-ze^{i \theta})(x - ze^{-i\theta})},$$
where $b$ and $c$ are non-zero complex numbers, $z = \frac{b}{\sqrt{bc}}$ and $\theta = \frac{...
- 43
1
vote
1
answer
327
views
Closed form expression for an integral
Let $\psi_q(z)$ be the q-DiGamma function defined for a complex variable $z$ with $\Re(z)>0$ as $$\psi_q(z)=\frac{1}{\Gamma_q(z)}\frac{\partial}{\partial z} (\Gamma_q(z))$$
where $\Gamma_q(z)$ is ...
- 910
1
vote
0
answers
76
views
Solving a set of implicit equations involving Polylogarithms
I have the following simultaneous equations:
\begin{aligned}
&H(\lambda) = a\, \text{Li}_{3/2}\left(b\frac{H(\lambda)}{F(\lambda)}\right), \; \\&H(\lambda) = c\, \text{Li}_{3/2}\left(d \, \...
4
votes
1
answer
145
views
Closed form expression for $\psi_{e^{\pi}}^{(3)}(1-i)$
Let $\psi_q(z)$ be the q-DiGamma function defined for a real variable $\Re(z)>0$ as $$\psi_q(z)=\frac{1}{\Gamma_q(z)}\frac{\partial}{\partial z} (\Gamma_q(z))$$
where $\Gamma_q(z)$ is the q-Gamma ...
- 910
0
votes
1
answer
132
views
Closed form expression for $\psi_{e^{\pi}}^{(3)}(1)$
Let $\psi_q(x)$ be the q-DiGamma function defined for a real variable $x>0$ as $$\psi_q(x)=\frac{1}{\Gamma_q(x)}\frac{\partial}{\partial x} (\Gamma_q(x))$$
where $\Gamma_q(x)$ is the q-Gamma ...
- 910
0
votes
1
answer
169
views
Is there a less time-consuming way to solve a Symmetric Matrix Equation
I'm currently working on solving an equation that involves a symmetric matrix C with 4 unknown variables, and a vector A of the same dimension. The equation I'm trying to solve is:
...
2
votes
0
answers
206
views
Wolfram Mathematica: why is the plot not visible?
simple question regarding Wolfram Mathematica:
Why is the plot not showing?
(See screenshot)
(I am new to Wolfram Mathematica)
Thankful for any input.
- 67
1
vote
0
answers
87
views
Integral of Dirac Delta Derivative Times Non-Smooth Function
I know that if we have some function f(y) that is smooth and has compact support, we get the following by using integration by parts.
$\int f(y) \delta '(y-x) dy = -\int f'(y) \delta (y-x) dy =-f'(x)$
...
- 157