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# Tag Info

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 ...

### 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 ...

### 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. ...
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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 ...

### 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 ...
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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] ...
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### Bilateral Laplace Transform

Update 2 In v12.3, BilateralLaplaceTransform and InverseBilateralLaplaceTransform are built-in. Their usages are almost the same ...
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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 ...

### 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. ...
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### Inverse Laplace Transform difficulty

InverseLaplaceTransform[(2 s^2 + s + 13)/((s - 1) ((s + 1)^2 + 4)), s, t] 2*E^t + (3/4)IE^((-1 - 2*I)t) (-1 + E^(4*I*t)) ...

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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 ...
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Maybe: ...

### Inverse Laplace transform

I was asked to explain how I arrived at the statement of my comment, regarding the first step of the complete solution. Here it is: The y-integral is of the form ...

### 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)....

### Mathematica and MATLAB giving different results from inverse Laplace transform

With Mathematica you can also do the following ...

As it explained in tutorials functions Radon and InverseRadon are supposed to be used with images only and not with arbitrary ...

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### LaplaceTransform works well with x[t], but doesn't recognize x[t], how to make it works for x[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: ...
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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: ...

### Calculate the Bromwich Integral (Inverse Laplace Transform)

This is decidedly not a general answer, but let's play a bit. If we do ...