# Tagged Questions

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### Mathematica 9 cannot solve this Integral. Mathematica 8 could. Is this a bug?

I was trying to (re)calculate a problem of an older Wolfram blog post (Problem 11457, by M. L. Glasser) with Mathematica 9.0.0.0 (on OS X 10.8.2). ...
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### Implementing discrete and continuous Hilbert transforms

What is an efficient and accurate Mathematica implementation of the Hilbert transform, for both continuous and especially discretely sampled functions? This transform relates phase and amplitude in ...
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### Numerical inverse Laplace-Hankel transform

When trying to reproduce the result of this paper about numerical solution of Lamb's problem, I encountered the following double integral (to be more precise, the 0-order inverse Hankel-Laplace ...
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### Laplace transform of $\frac{1-\cos (t)}{t}$

In the documentation, it states that The Laplace transform of a function $f(t)$ is defined to be $\int_0^{\infty } f(t) e^{-s t} \, \mathrm{d}t$. But why can Mathematica not get the Laplace ...
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### Computation of Hankel Transform using FFT (Fourier)

To address circularly symmetric cases of 2-D Fourier Transformations, the so-called Hankel Transform can be applied (for a detailed derivation of the relation between the 2-D Fourier transform and the ...
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### Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
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### Numerically obtaining the inverse Laplace transform of data

I have been using several Mathematica packages to do numerical inverse Laplace transforms on known (expressible in closed form) expressions, $\tilde{f}(s)$. I am now being confronted with the more ...
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### Workarounds for a possible bug in the linearity of FourierTransform

This is somewhat similar to this question, except the problem I am encountering is to do with Fourier transforms of scalar multiples of functions and their derivatives. I wish to input ...
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### Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
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### Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
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### Integrating over Bessel Function erroreous? (Hankel Transform)

Bug introduced in 8.0.4 or earlier and persists through 10.2. The Hankel Transform is given by Integrate[f[x] x BesselJ[0, x t], {x, 0, Infinity}] It is self-...
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### 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 $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
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### Integral of function involving Dirac delta

I am performing lots of simple calculations with dirac delta functions. It would be awesome if Mathematica could do this routine exercise for me, eliminating any possible human errors. For example, ...
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### Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

fixed in 10.0.2 Update I have tried like these. I think there is a bug. ...
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### 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 ...
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### Fourier Transform of Absolute Value

If you ask Mathematica to provide the Fourier Transform of a singular functions it is likely to provide an answer that while nearly correct, is technically incorrect and it will do so without a word ...
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### Incorrect output from InverseFourierTransform

Bug introduced in 8.0.4 or earlier and fixed in 9.0.1 or earlier I am trying to compute the inverse Fourier transform of this expression ...
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### Trouble with Fourier transform of Exp[-Sqrt[x]]

First time trying to do something "real" in Mathematica, I am having trouble getting it to calculate this Fourier transform. It runs for a long time, then just prints the input expression. ...
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### How to get a difference of two contour integrals depending on integer parameter?

I have two following functions: ...
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### Why does InverseFourierTransform gives different result to doing it by hand?

When I can calculate an inverse fourier transform by the built-in function InverserFourierTransform, the result is different from what I calculate by definition ...
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### Discrete Fourier Transform of a vector defined on a 3D lattice

In my research I need to compute the Discrete Fourier transform of a vector defined on a 3D lattice (a cube) to the "reciprocal" lattice. This is quite new to me so before proceeding i wanted to be ...
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### Unknown limit of an array of area integrals

Could someone explain why Mathematica can't finish computing this limit (this is a limit of an array, when n -> Infinity (n ...
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### Code for solving numerically an integro-differential equation

First of all, I want to greet the community. This is my first question, but I hope I will be able to help answering others members questions, although I am quite new working with Mathematica. I would ...
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### Inverse Z Transform returning complicated expression

I want to study how the Z transform changes with the sampling rate T, in a closed loop system. The command I'm using to do this is: ...
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### Indirect transformation based on a list of data points

I have a set of data which describes the Intensity function $Int(q)$ as a function of $q$. The data list provided below provides the shape of $Int(q)$ versus $q$.How can I use this information to ...
For this expression: $(1 - Exp[-Sqrt[1+s] x])/(1+s)$ How to make the Inverse Laplace Transform analytically? ...