18
votes
Accepted
Mathematica and MATLAB giving different results from inverse Laplace transform
You missed one term in Matlab. den=[1,4,2,3,0]; and not den=[1,4,2,3]; The order is important in Matlab. Since you do not have ...
- 149k
15
votes
Accepted
How to set up a spherically symmetric Fourier transform?
Summary: To perform the 3D Fourier Transform of a spherically symmetric function $f(r)$ in Mathematica, use the command
(4 Pi)/k FourierSinTransform[f[r] r, r, k]
...
- 15.3k
14
votes
Implement finite Fourier transforms
This post contains several code blocks, you can copy them easily with the help of importCode.
The following is my implementation for finite Fourier transforms. ...
- 67.6k
14
votes
Accepted
Wrong result of Laplace Transformation
Your integral is wrong. Laplace transform is defined from $0$ to $\infty$ not from $-\infty$ to $\infty$. The 2-sided Laplace transform is defined from $-\infty$ to $\infty$ but that is not the ...
- 149k
13
votes
Package for fast spherical harmonic transform in Mathematica?
I am aware that my answer would not be accepted because OP explicitly
demanded a FFT-like method.
I am aware of the fact that the method is not very fast either.
However, it is so simple that I do ...
- 19.3k
11
votes
Accepted
How can I invert a Laplace transform numerically?
As of v12.2, InverseLaplaceTransform supports numeric Laplace inversion. In addition, there exist at least 6 Mathematica packages for numeric inverse Laplace ...
- 67.6k
11
votes
Solving partial differential equation involving Hilbert transform
I used the method of solving integro-differential equations proposed by Michael E2 on Solving an integro-differential equation with Mathematica
I added new options to his code to solve this problem. ...
- 47.7k
10
votes
10
votes
Accepted
Correct way of simplifying the result of an integral
Many times Mathematica gives enormous results to simple problems
If Simplify still does not help reduce the antiderivative to what you like, you could always try ...
- 149k
10
votes
Accepted
9
votes
How to obtain that result of the integral in Mathematica?
It's a Fourier integral. With those, Mathematica can confidently venture into generalized function territory and yield things like DiracDelta (hazardous in general)....
- 13.9k
9
votes
Mathematica and MATLAB giving different results from inverse Laplace transform
With Mathematica you can also do the following
...
- 1,950
9
votes
InverseRadon behaves differently from iradon of MATLAB
As it explained in tutorials functions
Radon
and
InverseRadon
are supposed to be used with images only and not with arbitrary ...
- 47.7k
9
votes
3D Fourier transform of 1/r^2
The Fourier transform will be spherically symmetric, so let's set $\vec{k}$ parallel to the $z$-axis without restriction of generality.
First, generalize the integral to the Fourier transform of $r^{...
- 49.3k
8
votes
Accepted
8
votes
Accepted
InverseMellinTransform producing two different results for the same input?
expr = Gamma[1 + s]/Gamma[1 - s] Gamma[-s]^2;
imt1 = InverseMellinTransform[expr, s, x, GenerateConditions -> True]
...
- 161k
8
votes
Accepted
Inverting integral transform $f(s)=\int_0^\infty g(x) \exp(-s g(x)) \mathbb{d}x$
In the math.stackexchange post I have shown that
$$\left\{\theta(y-a)-\theta(y-b)\right\} \left(g^{-1}\right)^\prime(y)\, y=\mathcal{L}^{-1}[f](y)$$
where $g^{-1}$ is the inverse function $g^{-1}(g(x))...
- 19.3k
8
votes
Accepted
LaplaceTransform works well with x[t], but doesn't recognize x[1][t], how to make it works for x[1][t]?
Obviously a bug. (If I guess it right, it's introduced in v12.2 together with this bug. ) v9.0.1 gives the desired result:
A possible fix is turning to the method mentioned here:
...
- 67.6k
8
votes
Accepted
How to let Mathematica return impulse or Dirac delta functions when computing integrals?
If you use Dirac or Heaviside functions explicitly in your expression, Mathematica figures out that you're working with generalized functions. Unfortunately, it doesn't always work the other way: ...
- 13.9k
7
votes
Accepted
How to do continuous Fourier transform?
It looks like Mathematica can do this. Define something like this (I've simplified your version slightly)
...
- 16.8k
7
votes
Accepted
7
votes
InverseRadon behaves differently from iradon of MATLAB
As this has come up in the comments, somebody might be interested at least in the discrete version as described here: discrete radon transform:
getRadonLinesComped[] is the (compiled) function that ...
- 1,255
7
votes
Inverse Laplace Transform of Hypergeometric function
TL;DR: Convert to a MeijerG function using MeijerGReduce and apply the general formula found at : https://functions.wolfram.com/HypergeometricFunctions/MeijerG/22/...
- 5,947
6
votes
Accepted
Evaluating FourierTransform like integral manually
It looks like OP is interested in seeing how the integral can be done without using a black box like FourierTransform function. As mentioned in the comments, when ...
- 12.1k
6
votes
Accepted
Inverse Laplace transform of this complicated function
This post contains several code blocks, you can copy them easily with the help of importCode.
As already mentioned in the comment above, the deduction of $(1)$ is ...
- 67.6k
6
votes
Mathematica and MATLAB giving different results from inverse Laplace transform
With Mathematica, I get significantly different results than your Mathematica results. I do not have access to matlab nor know whether the matlab code shown is correct.
...
- 161k
6
votes
How to calculate an iterated derivative in Mathematica?
You are basically differentiating with respect to Log[x], which is possible using the ResourceFunction "ChainD":
...
- 131k
6
votes
3D Fourier transform of 1/r^2
Roman provides a perfect answer to the OP question. However, user64494 has some reservations claiming that the Fourier transform does not exist using as an argument calculations for the $\vec q=(1,1,1)...
- 19.3k
6
votes
Accepted
Differences in Mathematica's behaviour with identical functions
By typing 1.2*10^5 you are telling Mathematica to do things in floating point. Change this to 120000 and you get the desired exact form. To make it plot faster use Set (shortcut =) rather than ...
- 69.5k
6
votes
Accepted
Only top scored, non community-wiki answers of a minimum length are eligible