All Questions
Tagged with mathematica calculus
60
questions
0
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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
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
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
$$ \sum_{n=0}^{\infty} ...
- 17.5k
0
votes
0
answers
134
views
How can we prove that $x\Gamma(x)=1.$
how can we prove that, for $x$ real and positive, $lim_{x→0^+}$ $x\Gamma(x)=1.$
0
votes
0
answers
561
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Conversion of clockwise angle rotation to anticlockwise and vice versa
I have some data sets and using that data sets I'm trying to calculate the rotation numbers. Calculating rotation numbers I have to take some particular direction of vectors, i.e., either clockwise or ...
- 11
0
votes
1
answer
108
views
how to find minimum distance from a point to a graph using Mathematica?
Find the point on the graph of $y= x^{3/2}$ that is closest to the point $(4, 0)$.
This is an optimization problem. I used the distance formula.
$d=\sqrt{(4-x)^2+(0-x^{3/2})^2}$
$d^2=16-8x+x^2+x^3$
...
3
votes
3
answers
199
views
Trying to duplicate in Mathematica a graph from Ordinary Differential Equations by Tenenbaum and Pollard
In the textbook Ordinary Differential Equations by Tenenbaum and Pollard they have a graph of this eqn:
$x^3+y^3-3xy=0$
The graph is:
I've tried:
Plot[x^3 + y^3 - 3 xy = 0, {x, 0, 10}, {y, 0, 10}]
...
- 63
0
votes
2
answers
57
views
An explanation for the result of the following limit
Whilst having troubles in calculating the following limit, which I thought it were indeterminate, I decided to put it into W. Mathematica (the serious software, not W. Alpha online) and it returned ...
- 3,482
2
votes
1
answer
134
views
Madelung Constant
I have been working in this series
$$\sum _{m=0}^{\infty } \sum _{k=0}^{\infty } \sum _{j=0}^{\infty } \frac{(-1)^{j+k+m} \left((j+1)^2+(k+1)^2+(m+1)^2\right)}{\left((j+1)^2+(k+1)^2+(m+1)^2\right)^{3/...
- 357
1
vote
2
answers
139
views
Integration of quotient of hypergeometric functions
If one has an expression of the form,
$$\int \frac{\, _2F_1(a,b;c;z)}{_2F_1(d,e;f;z)}dz,$$
where the arguments are all complex numbers, is it possible to integrate this to get another hypergeometric ...
- 83
1
vote
1
answer
141
views
How to calculate the following expectation and variance?
Given
$$X_1 \sim N(\mu_1, \sigma_1^2),$$
$$X_2 \sim N(\mu_2, \sigma_2^2),$$
$$X_1 \mathrm{\ and\ } X_2 \mathrm{\ are\ independent}.$$
and
$$Y = \max(\max(X_1,0) + X_2, 0),$$
find
$$E(Y) \mathrm{\ \ ...
- 37
4
votes
0
answers
167
views
Solving a difficult integral
I have been stuck on the following integral for some time:
$$
I = \int^{2 \pi}_0 \mathrm{d}\theta \frac{\cos \theta\left(x + \Delta\cos\theta\right)}{\sqrt{k + \left(x + \Delta\cos\theta\right)^2}} \...
2
votes
1
answer
57
views
On simplifying large exponential equations
I'm working on undergrad research in fractal geometry and have to prove certain functions are decreasing, one of which is
$$g(x) = \frac{\left( \frac{2^m-2}{2^m-1}+ \frac{1}{2^m-1}\left(\frac{1}{2^m}...
- 174
1
vote
1
answer
67
views
Deriving the BBP identify for $\pi$
I was given a problem to learn how to use Mathematica. I should derive the identity from the paper 1 known as the BBP formula for $\pi$. But I can't figure it out why
$$\begin{equation} \sum_{k=0}^{\...
- 159
0
votes
0
answers
217
views
Computational examples in differential geometry using Mathematica, Matlab, Maple etc. with visualization possible
I want to master the computing "apparatus" of differential geometry. Some theoretical sections are already very difficult to assimilate, and without visual calculations it is almost impossible to ...
- 731