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32
votes
1answer
1k views

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). ...
14
votes
5answers
344 views

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 ...
8
votes
2answers
2k views

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 ...
8
votes
1answer
778 views

Computation of Hankel Transform using FFT (Fourier)

To address circular symmetric cases of 2D Fourier Transformations the so called Hankel Transform can be applied (for a detailed derivation of the relation between the 2D Fourier transform and the 1D ...
7
votes
0answers
448 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
3
votes
1answer
77 views

PrincipalValue option of Convolve not working in 9.0.1?

The PrincipalValue option of Convolve is used in this question to define the Hilbert transform. However, in Mathematica 9.0.1, ...
3
votes
1answer
290 views

Integrating over Bessel Function erroreous? (Hankel Transform)

The Hankel Transform is given by Integrate[f[x] x BesselJ[0,x t],{x,0,Infinity}] It is self-inverse, so ...
1
vote
2answers
65 views

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 ...
1
vote
0answers
67 views

Imaginary number appears in Integrate [closed]

I had a problem in the following code because when I use Integrate, there will always be imaginary number in the result. I put my code here. The satisfactory result should look like eq 9.138, which I ...
0
votes
1answer
332 views

Fourier series spectrum argument and absolute value [closed]

Started playing with Mathematica a week ago. Now I'm on some more "advanced" stuff and really can't figure out what is happening. I'm trying to get the spectrum of this signal, $x(t) = 110 ...
0
votes
1answer
124 views

Error Function Integral (Erf)

Any idea how to solve analytically this integral Integrate[(a Erf[a Sqrt[b/(a^2 + b)] c])/(a^2 + b)^(3/2), a] I tried substitution u=a^2 + b, but it didn't work. ...
0
votes
1answer
39 views

Z-Transforms and Floor Functions

When I take the $Z$-Transform of the Floor function: ZTransform[ Floor[x], x, z] I get ...
0
votes
0answers
27 views

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: ...
0
votes
0answers
53 views

Exponential function Integral

I have tried to solve this integral: Integrate[E^(-((a^2 b c^2)/(a^2 + b)))/(a^2 + b)^2,a] Mathemathica is not able to solve it, I have tried the integration by ...