All Questions
Tagged with mathematica real-analysis
15
questions
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
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
3
votes
0
answers
306
views
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 ...
- 560
1
vote
0
answers
83
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 ...
- 2,184
1
vote
1
answer
58
views
Hpergeometric Reduction with Mathematica
We know that:
$$\,_2F_1(a,b,b,z)=(1-z)^{-a}$$
But putting $b<0$ with $b$ integer Mathematica does not use the previous formula but generates the hypergeometric polynomial. For instance:
$$\,_2F_1(a,...
- 187
1
vote
1
answer
67
views
Deriving the BBP identify for $\pi$
I was given a problem to learn how to use Mathematica. I should derive the identity from the paper 1 known as the BBP formula for $\pi$. But I can't figure it out why
$$\begin{equation} \sum_{k=0}^{\...
- 159
1
vote
1
answer
73
views
Software which writes long math expressions in short form by detecting the patterns?
Is there any software which can detects the patterns in long math expression and collects them as sums and products in short form. I am working with some long expressions of the following forms. I ...
- 363
1
vote
1
answer
51
views
How to interpret this Mathematica command input as given in book?
I am unable to understand what the book stands for by the given command shown as input in Mathematica, as given at its Googlebooks limk here.
I mean the line given by:
$lim_{x\rightarrow \infty} cos2(...
- 4,532
0
votes
0
answers
68
views
Plot of a function given by an integral.
I want to plot the following integral as a function of $x$ but Mathematica fails to draw it even using the numerical integration.
$$f(x)=\displaystyle\int_0^{\infty } \left(\sum _{n=1}^{\infty } n^4e^{...
- 1,260
1
vote
0
answers
34
views
Determining the sign of a function containing ratio
Problem
We want to know for which values of $x,y,z,w$ the function $\sigma$ is positive or negative:
\begin{equation}
\sigma = \frac{A}{A^2-B^2},
\end{equation}
where
\begin{eqnarray}
A & = &...
- 587
6
votes
3
answers
168
views
Find min of $\frac{\left( \sum kx_k \right) \left( \sum x^2_k \right)}{\left( \sum x_k \right)^3}$
With $n \ge 2$ and $x_1,\ x_2,\ \dots,\ x_n > 0$. Find the minimum of:
$$ M = \frac{(x_1 + 2 x_2 + ...+ nx_n)( x^2_1 + x^2_2 +...+x^2_n)} {\left( x_1 + x_2 +...+ x_n \right)^3}$$
For specific $n$, ...
- 2,977
3
votes
0
answers
133
views
Solution of nonlinear waves( breathers)
The sine-Gordon equation is known as $$\frac{\partial^2 u}{\partial t^2} - \frac{\partial^2 u}{\partial x^2} + \sin u = 0,$$
Can you please derive the equation which is known as breather equation ...
user52950
4
votes
2
answers
917
views
Plotting graphs using numerical/mathematica method
From the author's equation 13, 14 We can write by inserting V''(A)=0,
Solving for R we get,
$$R= \frac{6^{D/4} \sqrt{D}}{\sqrt{-2^{1+\frac{D}{2}} 3^{D/2}+3 2^{1+D} A-3^{1+\frac{D}{2}} A^2}}$$
Now ...
user52950
1
vote
1
answer
463
views
Automated generation of a parametric plot?
Currently we are introducing integrals of manifolds in $3d$-Space in a course. We are given some set $E \subset \mathbb{R}^3$ and should evaluate the surface and scetch how it looks.
For example we ...
- 14k