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2
votes
2answers
66 views

How to do algebra on unsolved integrals?

I am working with functions calculated from a set of general basis functions. ...
1
vote
1answer
84 views

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. ...
0
votes
0answers
57 views

What's the wrong when I use the BodePlot?

I want to plot this Butterworth filter's TransferFunction: ...
5
votes
2answers
261 views

Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$

Update I have tried like these. I think there is a bug. Plot[1/Sqrt[-1 + 2^2 Sech[x]^2], {x, 0, ArcCosh[2]}, Ticks -> {{ArcCosh[2]}, Automatic}] This ...
2
votes
2answers
79 views

Integration of piecewise function

I'm trying to understand why Mathematica is not evaluating a piecewise function, while it's able to evaluate each of the regions separately. This fails: ...
1
vote
0answers
54 views

Inconsistent linearity of inverse Fourier transform

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 ...
0
votes
1answer
94 views

Solving Coulomb Integral [closed]

I am trying to solve so-called Coulomb Integral of two Gaussians: ...
0
votes
2answers
149 views

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 ...
0
votes
1answer
85 views

Inverse Laplace transform

For this expression: $ (1 - Exp[-Sqrt[1+s] x])/(1+s)$ How to make the Inverse Laplace Transform analytically? ...
0
votes
1answer
47 views

What should I expect for Fourier transform of Sinc? [closed]

I was expecting something I could interpret as a rect function. I don't think the Dirac delta function qualifies — for one thing, I think that would be the transform of a constant. ...
0
votes
0answers
67 views

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 ...
7
votes
3answers
499 views

Any way I can solve this integral?

So, Mathematica can't solve it. Any workaround? \begin{equation*} \int_0^\pi \frac{1}{\sin\left(\frac{\theta}{2}\right)^\beta + 1} \mathrm{d}\theta \end{equation*} The code is: ...
0
votes
0answers
63 views

Calculate inverse laplace transform by integration with four singular points?

I have a function U[s,x] to do inverse Laplace transform for analytical solution, as following ...
1
vote
1answer
136 views

Bilateral Laplace Transform in Mathematica (to be used with Moment Generating Functions)?

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
0
votes
1answer
66 views

Z-Transforms and Floor Functions

When I take the $Z$-Transform of the Floor function: ZTransform[ Floor[x], x, z] I get ...
1
vote
0answers
41 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: ...
1
vote
1answer
208 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
0answers
71 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 ...
1
vote
2answers
77 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 ...
14
votes
5answers
403 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 ...
3
votes
1answer
96 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, ...
9
votes
1answer
1k 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 ...
3
votes
1answer
380 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 ...
33
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). ...
7
votes
0answers
540 views

Inverse Laplace transform not obtained

I can't seem to be able to compute the inverse Laplace transform of a Laplace transform: ...
9
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 ...
16
votes
3answers
4k views

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 ...