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18 votes
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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 ...
Nasser's user avatar
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15 votes

Numerical inverse Laplace-Hankel transform

The following is not particularly fast and could be more accurate but does make progress toward the goals set in the Question. To begin, consider the analytical properties of ...
bbgodfrey's user avatar
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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. ...
xzczd's user avatar
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14 votes
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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] ...
Michael Seifert's user avatar
14 votes
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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 ...
Nasser's user avatar
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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 ...
yarchik's user avatar
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11 votes
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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 ...
xzczd's user avatar
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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. ...
Alex Trounev's user avatar
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10 votes

How to solve Laplace transform question for a system in Mathematica

...
rmw's user avatar
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10 votes
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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 ...
Nasser's user avatar
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10 votes
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Inverse Laplace Transform of Hypergeometric function

Maybe: ...
Mariusz Iwaniuk's user avatar
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)....
John Doty's user avatar
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9 votes

Mathematica and MATLAB giving different results from inverse Laplace transform

With Mathematica you can also do the following ...
rmw's user avatar
  • 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 ...
Alex Trounev's user avatar
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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^{...
Roman's user avatar
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8 votes
Accepted

How do I plot a Laplace transform?

Copying your exact code ...
nufaie's user avatar
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8 votes
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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] ...
Bob Hanlon's user avatar
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8 votes
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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))...
yarchik's user avatar
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8 votes
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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: ...
xzczd's user avatar
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8 votes
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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: ...
John Doty's user avatar
  • 13.7k
7 votes

Compute inverse Laplace transform with Integrate

Direct Integration Possible issues in performing the integrations include choice of Assumptions, branch cuts in the integrands, and how limits are taken. ...
bbgodfrey's user avatar
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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) ...
mikado's user avatar
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7 votes
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Finding the global maximum of a function

...
Bob Hanlon's user avatar
  • 159k
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 ...
Quit007's user avatar
  • 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/...
userrandrand's user avatar
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6 votes
Accepted

Possible incompatibility between ReplaceAll and LaplaceTransform

The issue here is that the replacement rule LHS evaluates: LaplaceTransform[u_, z, s] -> l[u] (* Out[1402]= u_/s -> l[u] *) To address this one can just ...
Daniel Lichtblau's user avatar
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 ...
Kagaratsch's user avatar
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 ...
xzczd's user avatar
  • 66.8k
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. ...
Bob Hanlon's user avatar
  • 159k
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": ...
Carl Woll's user avatar
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