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# Questions tagged [integral-transforms]

Questions about transforms of functions by means of integration, such as Fourier transforms and Laplace transforms. Many integral transforms can be inverted by means of another integral transform.

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381 views

### Mittag Leffler function Laplace transforms with Mathematica

Mathematica seems not to to know the basic Laplace and inverse Laplace relation $$\mathcal L(E_\alpha[−λt^α],t)(s)=\frac{s^{α-1}}{λ+s^α}$$ surrounding the Mittag Leffler function (...
32 views

### Verifying a cosine FourierTransform

On page 31 of this standard reference we have the following relation: I wanted to use mathematica to verify this transform numerically for some example values. So I type in: ...
190 views

### Fourier transform question

Consider the fourier transform FourierTransform[1/((Cosh[x] + 1) (Cosh[x]^2 - 1)^(1/2)), x, w] If I execute the above line, Mathematica thinks for several ...
135 views

### Integral Representation of DiracDelta

I would like to get dirac delta from integral definition, of course if I ask Integrate[Exp[I x t],{x,-Infinity,Infinity}] I get that the integral does not ...
198 views

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### Mathematica 11: Mellin transform conditions?

Consider the expression fun = 1/(y^2-1)^a; If I do the Mellin Transform explicitly, I get a result that involves a few conditions on the parameters ...
125 views

### Can Mathematica verify the Cahen - Mellin integral?

Can Mathematica verify the Cahen-Mellin integral? When I try Integrate[Gamma[1 + I s]/Zeta^(1 + I s), {s, -Infinity, Infinity}] I just get the input back. ...
507 views

### Region of convergence in Inverse laplace transform

Lets say we have a function in the s domain. Let it be H(s)=1/(s+1). It has one pole. If we consider the region to the right of the pole as the ROC, we would one function in the time domain when we ...
351 views

### How to find the Inverse Laplace transform of $Exp[(1-s)(1+1/s)]$? [closed]

How do i find the inverse laplace transform of following function: f[s]=Exp[(1-s)(1+1/s)] Mathematica returns exactly the simplified function without computing ...
76 views

### Understanding Mathematica's InverseZTransform Function

I'm trying to find the Inverse Z Transform of the following: InverseZTransform[(1 - ρ)/(1 - ρ z), z, n] and I get from Mathematica the result ...
117 views

### How do I implement custom integral transform with kernel $\cos^2 (zx)$ or $|\cos (zx)|$ in Mathematica?

I want a transform similar to Fourier transform but with a different kernel. With infinite limits: $$\int_{-\infty}^{\infty} f(x) \cos^2(zx)dx$$ I want it to work with distributions and other things,...
342 views

### Why does InverseLaplaceTranform give an incorrect solution?

Bug introduced in 9.0.1, fixed in 11.1. I was trying to answer this question, but I ended up asking this. Method 1 A workaround is to differentiate the ODE once, ...
166 views

### Implementation of the Riesz transform

Implementing the Hilbert transformation \begin{equation}H(f)(x) = \frac{1}{\pi}\lim_{\varepsilon \to 0} \int_{|x-y|>\varepsilon} \frac{1}{x-y}f(y) \, dy,\end{equation} appropriate for 1-...
293 views

### Why isn't Mathematica outputting the inverse fourier transform of this function?

I'm brand new to Mathmematica, so please be nice. I don't understand where I'm going wrong. I just need to use the method of inverse fourier transform on this wavefunction to get the momentum-space ...
158 views

### Inverse Laplace Transform Failing: $\frac{1}{\exp (\beta \tau )-a}$

I have tried various approaches to get the solution to this inverse transform but all so far are failing. ...
259 views

### Fourier transform of Exp[x]/x

Could you please explain why Mathematica gives the following expression when taking Fourier transform of $\exp(\lambda z)/\lambda$? $$\frac{-\log(-z)+\log(z)}{\sqrt{2\pi}}$$ Why the answer does not ...
254 views

1k views

### Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
298 views

263 views

### Convergence conditions of the Laplace Transform [closed]

I have to calculate some Laplace Integrals but if I use LaplaceTransform then it does not give the conditions when the integral converges. Is there an option to get ...
83 views

### Transfer function in recursive form [closed]

To get transfer function in recursive form, I tried this: ...
86 views

### How to get a difference of two contour integrals depending on integer parameter?

I have two following functions: ...
118 views

### Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
197 views

### Bilateral ZTransform

Is there support for bilateral Z-transform in Mathematica, or a third-party package?